[v23.3.x] Made storage::readers_cache size limitted

[vbotbuildovich]

Backport #16846 to branch v23.3.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 v23.3.x
git checkout -b vbotbuildovich/backport-16846-v23.3.x-53
git cherry-pick -x 427805735957293efd6dd9ff553fe55ef0922b56 4399ba422df04c1ac1cb2fc7fa4c5f9d352bda4d a494de610eb2a44045ad74553eced3dc5dd30714 d3b07defa19e25950524f31cb48dc4db310e8a37

git push origin vbotbuildovich/backport-16846-v23.3.x-53
gh pr create \
  --title "[v23.3.x] Made `storage::readers_cache` size limitted" \
  --base "v23.3.x" \
  --label "kind/backport" \
  --head "vbotbuildovich/backport-16846-v23.3.x-53" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v23.3.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/16846 "