[tests] Fix for stale Notification Center in Public UI tests when waiting for the messages

[vrubezhny]

No description provided.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 46.38%. Comparing base (da60441) to head (2045731).
⚠️ Report is 1769 commits behind head on main.

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #5849       +/-   ##
===========================================
+ Coverage   32.37%   46.38%   +14.00%     
===========================================
  Files          85      102       +17     
  Lines        6505     9391     +2886     
  Branches     1349     2105      +756     
===========================================
+ Hits         2106     4356     +2250     
- Misses       4399     5034      +635     
- Partials        0        1        +1     

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