Fix integration tests

[snejus]

This PR tightens the integration test workflow so CI runs the dependency-heavy checks that are usually skipped in local environments.

What changed

• Install the system packages and Poetry extras needed by integration-only coverage, including ffmpeg/ffprobe, ImageMagick/Pillow-backed art resizing, chroma, docs, replaygain, reflink, lyrics, and related plugin dependencies.
• Run poe docs before poe test in the integration workflow and set LYRICS_UPDATED=1 so lyrics tests are included in CI.
• Centralize CI detection in beets.test.helper.RUNNING_IN_CI and reuse shared import/program checks across test collection and helpers.
• Keep dependency-heavy tests strict in the beetbox GitHub Actions environment, while skipping them locally when optional tools/modules are unavailable.
• Mark ffprobe-, artresizer-, chroma-, pandoc-, and completion-related cases with focused availability gates so local test runs fail less often for missing optional dependencies.
• Update docs link-check ignores and stale documentation URLs so poe check-docs-links is less noisy in CI.

[Copilot]

Pull request overview

grug see PR change GitHub Actions integration test workflow trigger. it stop being only manual/weekly. it now run for pull request and push to master.

Changes:

• change integration_test.yaml trigger to run on pull_request
• add push trigger for master
• remove workflow_dispatch and weekly schedule trigger

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 74.52%. Comparing base (eaba5aa) to head (01792ec).
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6724      +/-   ##
==========================================
- Coverage   74.70%   74.52%   -0.19%     
==========================================
  Files         162      162              
  Lines       20822    20822              
  Branches     3298     3298              
==========================================
- Hits        15556    15517      -39     
- Misses       4507     4549      +42     
+ Partials      759      756       -3     

Files with missing lines	Coverage Δ
docs/conf.py	88.88% <ø> (ø)

... and 1 file with indirect coverage changes

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[github-actions]

Thank you for the PR! The changelog has not been updated, so here is a friendly reminder to check if you need to add an entry.