[v23.2.x] tx: add more trace logging in init_producer_id code path

[vbotbuildovich]

Backport #14401 to branch v23.2.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 v23.2.x
git checkout -b vbotbuildovich/backport-14401-v23.2.x-483
git cherry-pick -x 745d51690f708ee3a0d0a877a83f9c683bc6051c 6498739eacaf4b6ac2bc8a2f291fd6119816692f

git push origin vbotbuildovich/backport-14401-v23.2.x-483
gh pr create \
  --title "[v23.2.x] tx: add more trace logging in init_producer_id code path" \
  --base "v23.2.x" \
  --label "kind/backport" \
  --head "vbotbuildovich/backport-14401-v23.2.x-483" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --reviewer "ztlpn" \
  --milestone "v23.2.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/14401 "