[v25.1.x] cloud_io/cache: Prevent double counting of cache metrics

[vbotbuildovich]

Backport #28338 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-28338-v25.1.x-976
git cherry-pick -x c82e2b8c8b

git push origin manual-backport-28338-v25.1.x-976
gh pr create \
  --title "[v25.1.x] cloud_io/cache: Prevent double counting of cache metrics" \
  --base "v25.1.x" \
  --label "kind/backport" \
  --head "manual-backport-28338-v25.1.x-976" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v25.1.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/28338 "