Migrate publish GH action to the official pub.dev way of auth

.github/workflows/publish.yaml

@@ -1,37 +1,33 @@
-name: Publish new plugin version
+name: Publish new plugin version to pub.dev
+run-name: >-
+  [shared_storage] package publish (${{ github.ref_name }}) triggered by @${{ github.actor }}
+
 on:
-  workflow_dispatch:
   push:
-    branches:
-      - release
+    tags:
+      - "v[0-9]+.[0-9]+.[0-9]+"
 
+# Publish using custom workflow
 jobs:
   publish:
+    permissions:
+      id-token: write # This is required for authentication using OIDC
     runs-on: ubuntu-latest
-
+    defaults:
+      run:
+        working-directory: ./
     steps:
-      - uses: actions/checkout@v2
-      - uses: subosito/flutter-action@v2
-        with:
-          flutter-version: "3.7.7"
-          channel: "stable"
-      - run: |
-          flutter --version
-          flutter pub get
-          flutter analyze --fatal-infos
+      - uses: actions/checkout@v3
+      - uses: dart-lang/setup-dart@v1
+
+      - name: Install dependencies
+        run: dart pub get
 
-      - name: Create credentials file
-        run: echo $PUB_CREDENTIALS > ~/pub-credentials.json
-        env:
-          PUB_CREDENTIALS: ${{ secrets.PUB_CREDENTIALS }}
+      - name: Run Dart analyzer
+        run: dart analyze --fatal-infos
 
-      - name: Add credentials to Dart folder
-        run: |
-          mkdir -p ${XDG_CONFIG_HOME:-${HOME:-default}}/dart
-          touch ${XDG_CONFIG_HOME:-${HOME:-default}}/dart/pub-credentials.json
-          cp ~/pub-credentials.json ${XDG_CONFIG_HOME:-${HOME:-default}}/dart/pub-credentials.json
-        env:
-          PUB_CREDENTIALS: ${{ secrets.PUB_CREDENTIALS }}
+      - name: Run tests
+        run: dart test
 
       - name: Publish
         run: dart pub publish --force