[v24.1.x] [DEVEX-36] rpk: change expiry check for free_trial

[vbotbuildovich]

Backport #23951 to branch v24.1.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 v24.1.x
git checkout -b manual-backport-23951-v24.1.x-667
git cherry-pick -x 76dec5a2b7 84a3ff0fc2 663291e4c7

git push origin manual-backport-23951-v24.1.x-667
gh pr create \
  --title "[v24.1.x] [DEVEX-36] rpk: change expiry check for free_trial" \
  --base "v24.1.x" \
  --label "kind/backport" \
  --head "manual-backport-23951-v24.1.x-667" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v24.1.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/23951 "

[DEVEX-36]: https://redpandadata.atlassian.net/browse/DEVEX-36?atlOrigin=eyJpIjoiNWRkNTljNzYxNjVmNDY3MDlhMDU5Y2ZhYzA5YTRkZjUiLCJwIjoiZ2l0aHViLWNvbS1KU1cifQ