[BRE-1938] Update Build Web workflow to run on published Web releases

[vgrassia]

🎟️ Tracking

BRE-1938

📔 Objective

This PR updates the Build Web workflow to run on published Web releases that match the tag pattern web-v* instead of running on each published release in the monorepo. I also removed the Staged Rollout Desktop workflow since it has been migrated to the deploy repository.

📸 Screenshots

[github-actions]

🤖 Bitwarden Claude Code Review

Overall Assessment: APPROVE

This PR gates build-web.yml execution on release events whose tag matches web-v* and removes the migrated staged-rollout-desktop.yml. The new check-release-tag job writes a clear step summary for non-Web releases, and the setup job's if: correctly combines always() with a short-circuit OR so non-release triggers (pull_request, push, workflow_call, workflow_dispatch) proceed via result == 'skipped' while release events are gated by startsWith(github.event.release.tag_name, 'web-v'). Logic traces cleanly across all trigger types and the prefix used by the bash check matches the prefix in the startsWith gate.

Code Review Details

• ♻️ : Stale CODEOWNERS entry references the deleted workflow file
  • .github/CODEOWNERS:238 — staged-rollout-desktop.yml is deleted in this PR but still listed under the BRE team workflows section. GitHub silently ignores entries for missing files, so nothing breaks at runtime, but the line should be removed alongside the workflow deletion to keep CODEOWNERS in sync.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 47.46%. Comparing base (6b787c5) to head (566ce2f).
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@           Coverage Diff           @@
##             main   #20761   +/-   ##
=======================================
  Coverage   47.45%   47.46%           
=======================================
  Files        4004     4004           
  Lines      123162   123162           
  Branches    18947    18947           
=======================================
+ Hits        58448    58460   +12     
+ Misses      60287    60275   -12     
  Partials     4427     4427           

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[sonarqubecloud]

Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud