[v24.1.x] pandaproxy: add missing internal metrics

[vbotbuildovich]

Backport #24564 to branch v24.1.x. This issue was created as a placeholder because the original PR's commit(s) could not be automatically cherry-picked.
Here are the commands to execute:

git checkout v24.1.x
git checkout -b manual-backport-24564-v24.1.x-544
git cherry-pick -x b90c9f0f8d 939face46b

git push origin manual-backport-24564-v24.1.x-544
gh pr create \
  --title "[v24.1.x] pandaproxy: add missing internal metrics" \
  --base "v24.1.x" \
  --label "kind/backport" \
  --head "manual-backport-24564-v24.1.x-544" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v24.1.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/24564 "

JIRA Link: [CORE-8609](https://redpandadata.atlassian.net/browse/CORE-8609)