[v24.1.x] PESDLC0-1319 Log all kubectl command output

[vbotbuildovich]

Backport #18271 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-18271-v24.1.x-607
git cherry-pick -x aa1ac6ddcb5be7e2fc0a0a06240b6713331c6033 ab4b1f80d17a98ab2bf1ce12ac3579178978a624 214634a56b0f9ce3749fb06d6795f83e8aadda22

git push origin vbotbuildovich/backport-18271-v24.1.x-607
gh pr create \
  --title "[v24.1.x] PESDLC0-1319 Log all kubectl command output" \
  --base "v24.1.x" \
  --label "kind/backport" \
  --head "vbotbuildovich/backport-18271-v24.1.x-607" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v24.1.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/18271 "

JIRA Link: [CORE-2934](https://redpandadata.atlassian.net/browse/CORE-2934)