[v23.2.x] http: Fix double call to stop() in http::client

[vbotbuildovich]

Backport #18304 to branch v23.2.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 v23.2.x
git checkout -b vbotbuildovich/backport-18304-v23.2.x-684
git cherry-pick -x 2ed203deceffa1d560cdee64131b88f302069318

git push origin vbotbuildovich/backport-18304-v23.2.x-684
gh pr create \
  --title "[v23.2.x] http: Fix double call to stop() in http::client" \
  --base "v23.2.x" \
  --label "kind/backport" \
  --head "vbotbuildovich/backport-18304-v23.2.x-684" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v23.2.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/18304 "

JIRA Link: [CORE-2933](https://redpandadata.atlassian.net/browse/CORE-2933)