[v25.1.x] tests/kgo: handle errors when polling for verifier status

[vbotbuildovich]

Backport #27013 to branch v25.1.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 v25.1.x
git checkout -b manual-backport-27013-v25.1.x-830
git cherry-pick -x 9dff3196ee c7237ba7dd

git push origin manual-backport-27013-v25.1.x-830
gh pr create \
  --title "[v25.1.x] tests/kgo: handle errors when polling for verifier status" \
  --base "v25.1.x" \
  --label "kind/backport" \
  --head "manual-backport-27013-v25.1.x-830" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v25.1.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/27013 "

JIRA Link: [CORE-12958](https://redpandadata.atlassian.net/browse/CORE-12958)

[CORE-12958]: https://redpandadata.atlassian.net/browse/CORE-12958?atlOrigin=eyJpIjoiNWRkNTljNzYxNjVmNDY3MDlhMDU5Y2ZhYzA5YTRkZjUiLCJwIjoiZ2l0aHViLWNvbS1KU1cifQ