[Fixes #14242] Migrate groups endpoint to DRF

[nrjadkry]

Fixes #14242

Checklist

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[gemini-code-assist]

Code Review

This pull request introduces API filters, serializers, and viewsets for Group, GroupProfile, and GroupCategory models, alongside updated test cases and routing. The code review feedback highlights a correctness bug in GroupCategorySerializer.get_member_count where group profile IDs are incorrectly compared to category IDs. Additionally, the feedback recommends defensively handling missing request contexts in serializers and missing self.request attributes in viewsets to prevent potential KeyError and AttributeError exceptions during schema generation or background tasks.

[codecov]

Codecov Report

❌ Patch coverage is 90.00000% with 19 lines in your changes missing coverage. Please review.
✅ Project coverage is 74.96%. Comparing base (91c4ec5) to head (cfe7de4).
⚠️ Report is 11 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master   #14270      +/-   ##
==========================================
+ Coverage   74.92%   74.96%   +0.03%     
==========================================
  Files         975      977       +2     
  Lines       59902    60067     +165     
  Branches     8157     8171      +14     
==========================================
+ Hits        44884    45029     +145     
- Misses      13194    13205      +11     
- Partials     1824     1833       +9     

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