Search the public site through the API

Full-text on Postgres, stemmed in the language searched; word matching
elsewhere.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/Feature/Api/PublicApiContractTest.php

@@ -117,6 +117,7 @@ class PublicApiContractTest extends TestCase
             'testimonials' => ['path' => '/public/v1/testimonials', 'detail' => false],
             'talks' => ['path' => '/public/v1/talks', 'detail' => false],
             'technologies' => ['path' => '/public/v1/technologies', 'detail' => false],
+            'search' => ['path' => '/public/v1/search', 'detail' => true],
         ];
     }
 
@@ -133,6 +134,7 @@ class PublicApiContractTest extends TestCase
             '/public/v1/members/{slug}' => '/public/v1/members/ada-lovelace',
             '/public/v1/calls/{slug}' => '/public/v1/calls/backend',
             '/public/v1/services/{slug}' => '/public/v1/services/desarrollo',
+            '/public/v1/search' => '/public/v1/search?lang=es&q=proyecto',
         ];
     }