[v24.1.x] lw heartbeats during inflight appends

[vbotbuildovich]

Backport #19974 to branch v24.1.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 v24.1.x
git checkout -b vbotbuildovich/backport-19974-v24.1.x-191
git cherry-pick -x 4e926224134d35734e7d8dcaf5b276a9b2bec471 efc6c72fd5eb422a8f1a31af28b66d47e27d0a42 8663d4efa582ef154f672efe3dc839b6aa88f2c2 5fde255b592f197ee90dfe2e8964978150a27e2d 6619817decc79453900852d9943f8e93da6b148f

git push origin vbotbuildovich/backport-19974-v24.1.x-191
gh pr create \
  --title "[v24.1.x] lw heartbeats during inflight appends" \
  --base "v24.1.x" \
  --label "kind/backport" \
  --head "vbotbuildovich/backport-19974-v24.1.x-191" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v24.1.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/19974 "

JIRA Link: [CORE-4879](https://redpandadata.atlassian.net/browse/CORE-4879)