[v23.2.x] cloud_storage: use remote index in cloud timequery

[vbotbuildovich]

Backport #13011 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-13011-v23.2.x-688
git cherry-pick -x c1d03142dc993eb31d6ce67c7468fa83bdb31145 da8533ba5bd255fe41286e0d44013d60d93082d8 b78d7113406e05fade4975d76ee3efcc5b36dbf3 6d507cd0e3ee4849c531ff9e7bb3f2a90553b4e9 de5aa5345cd2449bb484be658574c3ab7a44d4ca

git push origin vbotbuildovich/backport-13011-v23.2.x-688
gh pr create \
  --title "[v23.2.x] cloud_storage: use  remote index in cloud timequery" \
  --base "v23.2.x" \
  --label "kind/backport" \
  --head "vbotbuildovich/backport-13011-v23.2.x-688" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --reviewer "Lazin,dotnwat" \
  --milestone "v23.2.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/13011 "