diff --git a/.github/workflows/package.yml b/.github/workflows/package.yml
deleted file mode 100644
index 6b55f10e..00000000
--- a/.github/workflows/package.yml
+++ /dev/null
@@ -1,76 +0,0 @@
-name: Test packaging
-
-on:
-  push:
-    branches:
-      - main
-  pull_request:
-  workflow_dispatch:
-
-permissions:
-  contents: read
-
-concurrency:
-  group: ${{ github.workflow }}-${{ github.head_ref || github.run_id }}
-  cancel-in-progress: true
-
-jobs:
-  wheel:
-    name: Test wheel install
-    runs-on: ubuntu-latest
-
-    steps:
-      - uses: actions/checkout@v4
-
-      - name: Set up Python
-        uses: actions/setup-python@v5
-        with:
-          python-version: 3
-
-      - name: Install pypa/build
-        run: |
-          # Be wary of running `pip install` here, since it becomes easy for us to
-          # accidentally pick up typing_extensions as installed by a dependency
-          python -m pip install --upgrade build
-          python -m pip list
-
-      - name: Build and install wheel
-        run: |
-          python -m build .
-          export path_to_file=$(find dist -type f -name "typing_extensions-*.whl")
-          echo "::notice::Installing wheel: $path_to_file"
-          pip install -vvv $path_to_file
-          python -m pip list
-
-      - name: Attempt to import typing_extensions
-        run: python -c "import typing_extensions; print(typing_extensions.__all__)"
-
-  sdist:
-    name: Test sdist install
-    runs-on: ubuntu-latest
-
-    steps:
-      - uses: actions/checkout@v4
-
-      - name: Set up Python
-        uses: actions/setup-python@v5
-        with:
-          python-version: 3
-
-      - name: Install pypa/build
-        run: |
-          # Be wary of running `pip install` here, since it becomes easy for us to
-          # accidentally pick up typing_extensions as installed by a dependency
-          python -m pip install --upgrade build
-          python -m pip list
-
-      - name: Build and install sdist
-        run: |
-          python -m build .
-          export path_to_file=$(find dist -type f -name "typing_extensions-*.tar.gz")
-          echo "::notice::Installing sdist: $path_to_file"
-          pip install -vvv $path_to_file
-          python -m pip list
-
-      - name: Attempt to import typing_extensions
-        run: python -c "import typing_extensions; print(typing_extensions.__all__)"
diff --git a/.github/workflows/publish.yml b/.github/workflows/publish.yml
new file mode 100644
index 00000000..9b69e73e
--- /dev/null
+++ b/.github/workflows/publish.yml
@@ -0,0 +1,149 @@
+# Based on
+# https://packaging.python.org/guides/publishing-package-distribution-releases-using-github-actions-ci-cd-workflows/
+
+name: Test builds and publish Python distribution to PyPI
+
+on:
+  release:
+    types: [published]
+  push:
+    branches: [main]
+  pull_request:
+
+permissions:
+  contents: read
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.head_ref || github.run_id }}
+  cancel-in-progress: true
+
+jobs:
+  build:
+    name: Build distribution
+    runs-on: ubuntu-latest
+
+    steps:
+      - uses: actions/checkout@v4
+      - name: Set up Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: "3.x"
+      - name: Check package metadata
+        run: python scripts/check_package.py ${{ github.ref }}
+      - name: Install pypa/build
+        run: |
+          # Be wary of running `pip install` here, since it becomes easy for us to
+          # accidentally pick up typing_extensions as installed by a dependency
+          python -m pip install --upgrade build
+          python -m pip list
+      - name: Build a binary wheel and a source tarball
+        run: python -m build
+      - name: Store the distribution packages
+        uses: actions/upload-artifact@v4
+        with:
+          name: python-package-distributions
+          path: dist/
+
+  test-wheel:
+    name: Test wheel
+    needs:
+      - build
+    runs-on: ubuntu-latest
+
+    steps:
+      - uses: actions/checkout@v4
+      - name: Set up Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: "3.x"
+      - name: Download all the dists
+        uses: actions/download-artifact@v4
+        with:
+          name: python-package-distributions
+          path: dist/
+      - name: Install wheel
+        run: |
+          export path_to_file=$(find dist -type f -name "typing_extensions-*.whl")
+          echo "::notice::Installing wheel: $path_to_file"
+          python -m pip install --user $path_to_file
+          python -m pip list
+      - name: Run typing_extensions tests against installed package
+        run: rm src/typing_extensions.py && python src/test_typing_extensions.py
+
+  test-sdist:
+    name: Test source distribution
+    needs:
+      - build
+    runs-on: ubuntu-latest
+
+    steps:
+      - uses: actions/checkout@v4
+      - name: Set up Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: "3.x"
+      - name: Download all the dists
+        uses: actions/download-artifact@v4
+        with:
+          name: python-package-distributions
+          path: dist/
+      - name: Unpack and test source distribution
+        run: |
+          export path_to_file=$(find dist -type f -name "typing_extensions-*.tar.gz")
+          echo "::notice::Unpacking source distribution: $path_to_file"
+          tar xzf $path_to_file -C dist/
+          cd ${path_to_file%.tar.gz}
+          python src/test_typing_extensions.py
+
+  test-sdist-installed:
+    name: Test installed source distribution
+    needs:
+      - build
+    runs-on: ubuntu-latest
+
+    steps:
+      - uses: actions/checkout@v4
+      - name: Set up Python
+        uses: actions/setup-python@v4
+        with:
+          python-version: "3.x"
+      - name: Download all the dists
+        uses: actions/download-artifact@v4
+        with:
+          name: python-package-distributions
+          path: dist/
+      - name: Install source distribution
+        run: |
+          export path_to_file=$(find dist -type f -name "typing_extensions-*.tar.gz")
+          echo "::notice::Installing source distribution: $path_to_file"
+          python -m pip install --user $path_to_file
+          python -m pip list
+      - name: Run typing_extensions tests against installed package
+        run: rm src/typing_extensions.py && python src/test_typing_extensions.py
+
+  publish-to-pypi:
+    name: >-
+      Publish Python distribution to PyPI
+    if: github.event_name == 'release' # only publish to PyPI on releases
+    needs:
+      - test-sdist
+      - test-sdist-installed
+      - test-wheel
+      - build
+    runs-on: ubuntu-latest
+    environment:
+      name: publish
+      url: https://pypi.org/p/typing-extensions
+    permissions:
+      id-token: write # IMPORTANT: mandatory for trusted publishing
+
+    steps:
+      - name: Download all the dists
+        uses: actions/download-artifact@v4
+        with:
+          name: python-package-distributions
+          path: dist/
+      - name: Ensure exactly one sdist and one wheel have been downloaded
+        run: test $(ls *.tar.gz | wc -l) = 1 && test $(ls *.whl | wc -l) = 1
+      - name: Publish distribution to PyPI
+        uses: pypa/gh-action-pypi-publish@release/v1
diff --git a/pyproject.toml b/pyproject.toml
index 4b1a7601..a59c9a0b 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -39,6 +39,7 @@ classifiers = [
     "Programming Language :: Python :: 3.10",
     "Programming Language :: Python :: 3.11",
     "Programming Language :: Python :: 3.12",
+    "Programming Language :: Python :: 3.13",
     "Topic :: Software Development",
 ]
 
diff --git a/scripts/check_package.py b/scripts/check_package.py
new file mode 100644
index 00000000..f52df411
--- /dev/null
+++ b/scripts/check_package.py
@@ -0,0 +1,60 @@
+import argparse
+import re
+import sys
+import tomllib
+from pathlib import Path
+
+
+class ValidationError(Exception):
+    pass
+
+
+def check(github_ref: str | None) -> None:
+    pyproject = Path(__file__).parent.parent / "pyproject.toml"
+    if not pyproject.exists():
+        raise ValidationError("pyproject.toml not found")
+    with pyproject.open("rb") as f:
+        data = tomllib.load(f)
+    pyproject_version = data["project"]["version"]
+
+    if github_ref is not None and github_ref.startswith("refs/tags/"):
+        version = github_ref.removeprefix("refs/tags/")
+        if version != pyproject_version:
+            raise ValidationError(
+                f"Version mismatch: GitHub ref is {version}, "
+                f"but pyproject.toml is {pyproject_version}"
+            )
+
+    requires_python = data["project"]["requires-python"]
+    assert sys.version_info[0] == 3, "Rewrite this script when Python 4 comes out"
+    match = re.fullmatch(r">=3\.(\d+)", requires_python)
+    if not match:
+        raise ValidationError(f"Invalid requires-python: {requires_python!r}")
+    lowest_minor = int(match.group(1))
+
+    description = data["project"]["description"]
+    if not description.endswith(f"3.{lowest_minor}+"):
+        raise ValidationError(f"Description should mention Python 3.{lowest_minor}+")
+
+    classifiers = set(data["project"]["classifiers"])
+    for should_be_supported in range(lowest_minor, sys.version_info[1] + 1):
+        if (
+            f"Programming Language :: Python :: 3.{should_be_supported}"
+            not in classifiers
+        ):
+            raise ValidationError(
+                f"Missing classifier for Python 3.{should_be_supported}"
+            )
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser("Script to check the package metadata")
+    parser.add_argument(
+        "github_ref", type=str, help="The current GitHub ref", nargs="?"
+    )
+    args = parser.parse_args()
+    try:
+        check(args.github_ref)
+    except ValidationError as e:
+        print(e)
+        sys.exit(1)
diff --git a/src/test_typing_extensions.py b/src/test_typing_extensions.py
index ae6ad076..5d37b5bf 100644
--- a/src/test_typing_extensions.py
+++ b/src/test_typing_extensions.py
@@ -1,5 +1,4 @@
 import sys
-import os
 import abc
 import gc
 import io
@@ -5718,8 +5717,7 @@ def test_typing_extensions_defers_when_possible(self):
                     getattr(typing, item))
 
     def test_typing_extensions_compiles_with_opt(self):
-        file_path = os.path.join(os.path.dirname(os.path.realpath(__file__)),
-                                 'typing_extensions.py')
+        file_path = typing_extensions.__file__
         try:
             subprocess.check_output(f'{sys.executable} -OO {file_path}',
                                     stderr=subprocess.STDOUT,