fix: Livechat popout not syncing department and custom fields

[dionisio-bot]

Backport of #36125

[changeset-bot]

⚠️ No Changeset found

Latest commit: fb02d93

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[dionisio-bot]

Looks like this PR is not ready to merge, because of the following issues:

• This PR is targeting the wrong base branch. It should target 7.7.0, but it targets 7.7.1

Please fix the issues and try again

If you have any trouble, please check the PR guidelines

[github-actions]

PR Preview Action v1.6.1
🚀 View preview at https://RocketChat.github.io/Rocket.Chat/pr-preview/pr-36299/
Built to branch gh-pages at 2025-06-24 19:13 UTC. Preview will be ready when the GitHub Pages deployment is complete.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 64.66%. Comparing base (8874a5a) to head (fb02d93).
Report is 1 commits behind head on release-7.7.2.

Additional details and impacted files

@@                Coverage Diff                @@
##           release-7.7.2   #36299      +/-   ##
=================================================
+ Coverage          64.48%   64.66%   +0.18%     
=================================================
  Files               3297     3259      -38     
  Lines             107785    96366   -11419     
  Branches           20070    18192    -1878     
=================================================
- Hits               69508    62318    -7190     
+ Misses             35450    31116    -4334     
- Partials            2827     2932     +105     

Flag	Coverage Δ
e2e	58.42% <ø> (+0.78%)	⬆️
unit	71.53% <ø> (+2.38%)	⬆️

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