Show library tracks in the Recently played playlist (#6161)

# What does this implement/fix?

The built-in "Recently played tracks" playlist stayed empty for anyone
starting playback from the Music Assistant UI. A track played from your
own library is recorded against the library rather than a streaming
service, and the playlist dropped every entry recorded that way, so it
never showed anything. Scrobbling to services like ListenBrainz kept
working throughout, which made it look like only the playlist was
affected.

- Library tracks now show up in "Recently played tracks" instead of
being silently skipped
- A track deleted from the library after it was played is left out
rather than breaking the playlist

**Related issue (if applicable):**

- related issue music-assistant/support#6290

## Types of changes

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- [x] Bugfix (non-breaking change which fixes an issue) — `bugfix`
- [ ] New feature (non-breaking change which adds functionality) —
`new-feature`
- [ ] Enhancement to an existing feature — `enhancement`
- [ ] New music/player/metadata/plugin provider — `new-provider`
- [ ] Breaking change (fix or feature that would cause existing
functionality to not work as expected) — `breaking-change`
- [ ] Refactor (no behaviour change) — `refactor`
- [ ] Documentation only — `documentation`
- [ ] Maintenance / chore — `maintenance`
- [ ] CI / workflow change — `ci`
- [ ] Dependencies bump — `dependencies`

## Checklist

- [x] The code change is tested and works locally.
- [x] `pre-commit run --all-files` passes.
- [x] `pytest` passes, and tests have been added/updated under `tests/`
where applicable.
- [ ] For changes to shared models, the companion PR in
`music-assistant/models` is linked.
- [ ] For changes affecting the UI, the companion PR in
`music-assistant/frontend` is linked.
- [x] I have read and complied with the project's [AI
Policy](https://github.com/music-assistant/.github/blob/main/AI_POLICY.md)
for any AI-assisted contributions.
- [ ] I have [raised a PR against the documentation
repository](https://github.com/music-assistant/music-assistant.io/blob/main/CONTRIBUTING.md)
targeting the main or beta branch as appropriate.

---------

Co-authored-by: Claude Fable 5.1 <[email protected]>