[v23.3.x] CORE-6860 Schema Registry: add detailed verbose compatibility checks

[vbotbuildovich]

Backport #22958 to branch v23.3.x. Note that this issue was created as a placeholder, since 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 vbotbuildovich/backport-22958-v23.3.x-559
git cherry-pick -x 11a87c3578ad396514bb8299bebeb5024ae37d1c ffecdd1a3f71256d08f5984d7590780cbfb95227 4c87c5ed21416d98f6d05a1c6c06ec0ab4949336 cda768b4a3da734f52ab04b5220c4d93b7e5fd97

git push origin vbotbuildovich/backport-22958-v23.3.x-559
gh pr create \
  --title "[v23.3.x] CORE-6860 Schema Registry: add detailed verbose compatibility checks" \
  --base "v23.3.x" \
  --label "kind/backport" \
  --head "vbotbuildovich/backport-22958-v23.3.x-559" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v23.3.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/22958 "

JIRA Link: [CORE-7075](https://redpandadata.atlassian.net/browse/CORE-7075)

[BenPope]

Fixed by #23170