Adds a GitHub Actions workflow that cherry-picks merged PRs to the
latest release branch when the `cherry-pick` label is applied.

## How it works

1. Add the `cherry-pick` label to any PR targeting `main` (before or
after merge).
2. On merge (or on label if already merged), the workflow detects the
latest `release/*` branch.
3. It cherry-picks the merge commit (`-x -m1`) and opens a PR.

This complements the `backport` label (see #24025) which targets the
latest **3** release branches. `cherry-pick` targets only the **latest**
one — useful for getting fixes into the current release.

Created PRs follow existing repo conventions:
- **Branch:** `backport/<pr>-to-<version>`
- **Title:** `<original PR title> (#<pr>)` — e.g. `fix(site): correct
button alignment (#12345)`
- **Body:** links back to the original PR and merge commit

If the cherry-pick encounters conflicts, the workflow aborts the
cherry-pick, creates an empty commit with resolution instructions, and
opens the PR with a `[CONFLICT]` prefix so the author can resolve
manually.

Also:
- Removes `scripts/backport-pr.sh` (replaced by this workflow)
- Removes `.github/cherry-pick-bot.yml` (old bot config)
- Adds a section to the contributing docs explaining the `cherry-pick`
label

> [!NOTE]
> Generated with [Coder Agents](https://coder.com/agents)

(cherry picked from commit ab77154)