Cherry-pick publishing changes to release/stable

[bhimrazy]

What does this PR do?

Corrects #21701, which was targeted at release/2.6.x instead of release/stable.

release/stable is the active release branch — it currently serves the same purpose as release/2.6.x, making the latter redundant. release/2.6.x(outdated) will be deleted after this lands. The branch will only be needed again when we bump to 2.7, at which point release/stable will be renamed to release/2.6.x.

Already present in release/stable — skipped:

• fix: resolve pkg-resources deprecation issue #21538 — fix: resolve pkg-resources deprecation issue
• Bump pyyaml in CI #21558 — Bump pyyaml in CI

Cherry-picked in this PR:

• Setup package publishing via PyPi Trusted Publisher Management #21594 — Setup package publishing via PyPi Trusted Publisher Management
• Docs: avoid unresolved torch.jit Sphinx refs to fix the CICD doc build failure. #21621 — Docs: avoid unresolved torch.jit Sphinx refs
• Update auto-label-merge-conflicts action to latest version
• ci: temporarily disable litbot checkgroup (+ follow-up)
• Update version from 2.6.1 to 2.6.4 #21715 — Update version from 2.6.1 to 2.6.4

Before submitting

• Was this discussed/agreed via a GitHub issue? (not for typos and docs)
• Did you read the contributor guideline, Pull Request section?
• Did you make sure your PR does only one thing, instead of bundling different changes together?
• Did you make sure to update the documentation with your changes? (if necessary)
• Did you write any new necessary tests? (not for typos and docs)
• Did you verify new and existing tests pass locally with your changes?
• Did you list all the breaking changes introduced by this pull request?
• Did you update the CHANGELOG? (not for typos, docs, test updates, or minor internal changes/refactors)

PR review

Anyone in the community is welcome to review the PR.
Before you start reviewing, make sure you have read the review guidelines. In short, see the following bullet-list:

Reviewer checklist

• Is this pull request ready for review? (if not, please submit in draft mode)
• Check that all items from Before submitting are resolved
• Make sure the title is self-explanatory and the description concisely explains the PR
• Add labels and milestones (and optionally projects) to the PR so it can be classified

[codecov-commenter]

⚠️ Please install the to ensure uploads and comments are reliably processed by Codecov.

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 79%. Comparing base (458c50a) to head (d802435).
⚠️ Report is 1 commits behind head on release/stable.
✅ All tests successful. No failed tests found.
❗ Your organization needs to install the Codecov GitHub app to enable full functionality.

❗ There is a different number of reports uploaded between BASE (458c50a) and HEAD (d802435). Click for more details.

HEAD has 164 uploads less than BASE

Flag	BASE (458c50a)	HEAD (d802435)
cpu	83	42
python	6	3
lightning_fabric	26	0
pytest	41	0
python3.12	24	12
python3.13	17	9
python3.10	6	3
lightning	30	15
python3.11	12	6
python3.12.7	18	9

Additional details and impacted files

@@                Coverage Diff                @@
##           release/stable   #21727     +/-   ##
=================================================
- Coverage              87%      79%     -8%     
=================================================
  Files                 270      267      -3     
  Lines               23888    23829     -59     
=================================================
- Hits                20665    18758   -1907     
- Misses               3223     5071   +1848