[v23.3.x] schema_registry: Add metrics

[vbotbuildovich]

Backport #23794 to branch v23.3.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 v23.3.x
git checkout -b manual-backport-23794-v23.3.x-990
git cherry-pick -x 7434dd8ef5 a8b6f460a3 7a2d9c2a44

git push origin manual-backport-23794-v23.3.x-990
gh pr create \
  --title "[v23.3.x] schema_registry: Add metrics" \
  --base "v23.3.x" \
  --label "kind/backport" \
  --head "manual-backport-23794-v23.3.x-990" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v23.3.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/23794 "