[Backport 2.x] [workspace] update search bar layout and align workspace selector

[opensearch-trigger-bot]

Backport 79fed30 from #8649.

[github-actions]

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[codecov]

Codecov Report

Attention: Patch coverage is 78.72340% with 10 lines in your changes missing coverage. Please review.

Project coverage is 60.92%. Comparing base (a0b42c6) to head (cdbbc5d).
Report is 1 commits behind head on 2.x.

Files with missing lines	Patch %	Lines
...core/public/chrome/ui/header/header_search_bar.tsx	89.47%	3 Missing and 1 partial ⚠️
.../components/global_search/search_pages_command.tsx	42.85%	2 Missing and 2 partials ⚠️
...pace/public/components/global_search/page_item.tsx	0.00%	2 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##              2.x    #8687   +/-   ##
=======================================
  Coverage   60.92%   60.92%           
=======================================
  Files        3787     3787           
  Lines       90310    90315    +5     
  Branches    14156    14161    +5     
=======================================
+ Hits        55020    55026    +6     
+ Misses      31818    31816    -2     
- Partials     3472     3473    +1     

Flag	Coverage Δ
Linux_1	29.03% <6.38%> (+<0.01%)	⬆️
Linux_2	56.54% <89.47%> (+0.01%)	⬆️
Linux_3	37.71% <0.00%> (+<0.01%)	⬆️
Linux_4	29.94% <0.00%> (+<0.01%)	⬆️
Windows_1	29.04% <6.38%> (+<0.01%)	⬆️
Windows_2	56.50% <89.47%> (+0.01%)	⬆️
Windows_3	37.71% <0.00%> (+<0.01%)	⬆️
Windows_4	29.94% <0.00%> (+<0.01%)	⬆️

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