[v23.3.x] c/balancer_backend: first initialize planner and then call plan

[vbotbuildovich]

Backport #18091 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-18091-v23.3.x-431
git cherry-pick -x a52d0ada31dd0c842333fadc2efc37d4aaf2b471

git push origin vbotbuildovich/backport-18091-v23.3.x-431
gh pr create \
  --title "[v23.3.x] c/balancer_backend: first initialize planner and then call plan" \
  --base "v23.3.x" \
  --label "kind/backport" \
  --head "vbotbuildovich/backport-18091-v23.3.x-431" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v23.3.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/18091 "

JIRA Link: [CORE-2693](https://redpandadata.atlassian.net/browse/CORE-2693)

[CORE-2693]: https://redpandadata.atlassian.net/browse/CORE-2693?atlOrigin=eyJpIjoiNWRkNTljNzYxNjVmNDY3MDlhMDU5Y2ZhYzA5YTRkZjUiLCJwIjoiZ2l0aHViLWNvbS1KU1cifQ