[2.x] Recreate the HydeSearch plugin with Alpine.js

[caendesilva]

Replaces the HydeSearch plugin with an Alpine.js and Blade implementation to make it more customizable and to reduce external dependencies. It also lets us more easily couple fixes and improvements to Hyde versions.

• Targets [2.x] New asset system #2006

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (4575d7f) to head (5782c86).
Report is 31 commits behind head on refactor-hydefront-styles-to-tailwind.

Additional details and impacted files

@@                            Coverage Diff                            @@
##             refactor-hydefront-styles-to-tailwind     #2029   +/-   ##
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  Coverage                                   100.00%   100.00%           
  Complexity                                    1906      1906           
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  Files                                          195       195           
  Lines                                         5078      5078           
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  Hits                                          5078      5078           

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[caendesilva]

I think it makes sense to hide the keyboard shortcut help text when there are search results, for a few reasons:

1. Once users are actively searching/viewing results, the shortcuts become less relevant
2. The space could be better used for showing more results
3. There are multiple obvious ways to exit the modal:
   • The ESC key (which is a common pattern across the web)
   • Clicking the X button in the header
   • Clicking outside the modal (click-away behavior)
   • The search button is still visible