[v25.2.x] Data migrations worker rework

[vbotbuildovich]

Backport #27014 to branch v25.2.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 v25.2.x
git checkout -b manual-backport-27014-v25.2.x-434
git cherry-pick -x 3beb2f0d98 d9f07a7bc2 12a4420c7a

git push origin manual-backport-27014-v25.2.x-434
gh pr create \
  --title "[v25.2.x] Data migrations worker rework" \
  --base "v25.2.x" \
  --label "kind/backport" \
  --head "manual-backport-27014-v25.2.x-434" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v25.2.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/27014 "

JIRA Link: [CORE-12967](https://redpandadata.atlassian.net/browse/CORE-12967)

[CORE-12967]: https://redpandadata.atlassian.net/browse/CORE-12967?atlOrigin=eyJpIjoiNWRkNTljNzYxNjVmNDY3MDlhMDU5Y2ZhYzA5YTRkZjUiLCJwIjoiZ2l0aHViLWNvbS1KU1cifQ