feat: migrate DocSearch to Algolia autocomplete

[9renpoto]

Summary

• replace DocSearch integration with Algolia autocomplete-based search UI
• rename island component to AlgoliaSearch and update Header usage
• switch dependencies to @algolia/autocomplete-js and algoliasearch/lite (v5)
• update styles and README for Algolia-based search

Validation

• deno task lint
• deno task test
• deno task build

[codecov]

Codecov Report

❌ Patch coverage is 24.50980% with 77 lines in your changes missing coverage. Please review.
✅ Project coverage is 78.08%. Comparing base (b40890c) to head (d08e699).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
islands/AlgoliaSearch.tsx	14.44%	76 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #168      +/-   ##
==========================================
- Coverage   86.68%   78.08%   -8.60%     
==========================================
  Files          19       19              
  Lines         488      543      +55     
  Branches       34       34              
==========================================
+ Hits          423      424       +1     
- Misses         53      107      +54     
  Partials       12       12              

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.