[v23.3.x] producer_state: add request::set_error and make it idempotent

[vbotbuildovich]

Backport https://github.com/redpanda-data/redpanda/pull/19783 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-19783-v23.3.x-211
  git cherry-pick -x 110002cf4950f73de89abf6bcd782700aca0891d 5fe079a2fedac63c4cd6fef2618746856b48eb37 7579cf1633e1b8e2e031afacec777085ffb03811 7719140e3ad316d3b8cde523b61f7601a7389bcf

  git push origin vbotbuildovich/backport-19783-v23.3.x-211
  gh pr create \
    --title "[v23.3.x] producer_state: add request::set_error and make it idempotent " \
    --base "v23.3.x" \
    --label "kind/backport" \
    --head "vbotbuildovich/backport-19783-v23.3.x-211" \
    --draft \
    --repo "redpanda-data/redpanda" \
    --milestone "v23.3.x-next" \
    --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/19783 "

JIRA Link: [CORE-4195](https://redpandadata.atlassian.net/browse/CORE-4195)

[BenPope]

Fixed by #21526