[v24.3.x] [CORE-8754] Handle new TLS error codes

[vbotbuildovich]

Backport #24749 to branch v24.3.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 v24.3.x
git checkout -b manual-backport-24749-v24.3.x-761
git cherry-pick -x ad6d50c0bd 0803e0d920

git push origin manual-backport-24749-v24.3.x-761
gh pr create \
  --title "[v24.3.x] [CORE-8754] Handle new TLS error codes" \
  --base "v24.3.x" \
  --label "kind/backport" \
  --head "manual-backport-24749-v24.3.x-761" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v24.3.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/24749 "

[CORE-8754]: https://redpandadata.atlassian.net/browse/CORE-8754?atlOrigin=eyJpIjoiNWRkNTljNzYxNjVmNDY3MDlhMDU5Y2ZhYzA5YTRkZjUiLCJwIjoiZ2l0aHViLWNvbS1KU1cifQ

JIRA Link: [CORE-8782](https://redpandadata.atlassian.net/browse/CORE-8782)