#7420: Drop updateSidebar call from browserAction.onClick

[fregante]

What does this PR do?

• Fixes the first piece of MV2 sidebar regressions #7420

Checklist

• Add tests
• New files added to src/tsconfig.strictNullChecks.json (if possible)
• Designate a primary reviewer: @grahamlangford

Follows

• #7228: Add support for sidePanel in the MV3 build #7354

[codecov]

Codecov Report

Attention: 4 lines in your changes are missing coverage. Please review.

Comparison is base (808cbc8) 72.60% compared to head (297926c) 72.61%.

Files	Patch %	Lines
src/contentScript/sidebarDomControllerLite.ts	0.00%	3 Missing ⚠️
src/background/browserAction.ts	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #7428      +/-   ##
==========================================
+ Coverage   72.60%   72.61%   +0.01%     
==========================================
  Files        1212     1212              
  Lines       37846    37839       -7     
  Branches     7099     7100       +1     
==========================================
- Hits        27479    27478       -1     
+ Misses      10367    10361       -6     

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[github-actions]

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