fix(ui): updated unread indicator to use core badge widget

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Linear: FLU-404

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 64.90%. Comparing base (5a9cc18) to head (94228dc).
⚠️ Report is 1 commits behind head on feat/design-refresh.

Additional details and impacted files

@@                   Coverage Diff                   @@
##           feat/design-refresh    #2546      +/-   ##
=======================================================
- Coverage                64.90%   64.90%   -0.01%     
=======================================================
  Files                      437      437              
  Lines                    26677    26673       -4     
=======================================================
- Hits                     17315    17311       -4     
  Misses                    9362     9362              

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