[v23.3.x] Wire `transform::logging::manager` into transform API, rpc client

[vbotbuildovich]

Backport #16485 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-16485-v23.3.x-310
git cherry-pick -x 9e357d16ce4b0c174524aed1c876f59e7d817681 64637993d9fd58ef675c0ac15d4678886368a3f6 91ce99ec62ed2aeb0e342dd859e9bd7baffceb19 c41eaa1a64f6a440f2fb18e14b0cb63a44a3160b d59c9283593eb11f95667a16a1f5df27ccb97e3a 5280839a4331e08668b1ff0bb0bcc9324b1625c9 f0369517885112df742c949ef75990cbd82cf625 a637233f124fc95d9f3c7ff2011e8e6e1635a333 ddea1e2bc42ac730a355e188c9ce876f2940bcfa 9562bbdfd1010182f1699c3d72d20a32130fec0b 38f99f9c9dbdda98041f1f81dbb95d2e1e3ebead ad2c4e6b2dc94e2763e6018da2388a95d46c62bc a7f6ba087f356d03314794dd7da1a00e6c48a91d

git push origin vbotbuildovich/backport-16485-v23.3.x-310
gh pr create \
  --title "[v23.3.x] Wire `transform::logging::manager` into transform API, rpc client" \
  --base "v23.3.x" \
  --label "kind/backport" \
  --head "vbotbuildovich/backport-16485-v23.3.x-310" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v23.3.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/16485 "

[oleiman]

@rockwotj - Spoke briefly to @piyushredpanda who agreed that we can probably hold off backporting this until supporting rpk pieces are in place. Lmk if you think of a compelling reason to get this into 23.3.x sooner.

[rockwotj]

SGTM

[oleiman]

Must include #16572