[v23.3.x] CORE-6835 Fix first time compacted segment upload

[vbotbuildovich]

Backport #22812 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-22812-v23.3.x-576
git cherry-pick -x 9bbe429c73f52da28a8749cc7b2462f85f6c17be de013217e1887ca87330144695bfd6cb94dbb589 e2fd9806a13c916cb7a090847754976b18018437

git push origin vbotbuildovich/backport-22812-v23.3.x-576
gh pr create \
  --title "[v23.3.x] CORE-6835 Fix first time compacted segment upload" \
  --base "v23.3.x" \
  --label "kind/backport" \
  --head "vbotbuildovich/backport-22812-v23.3.x-576" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v23.3.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/22812 "

JIRA Link: [CORE-6954](https://redpandadata.atlassian.net/browse/CORE-6954)

[piyushredpanda]

Closing as won't do.