feat(web-search): switch Perplexity to native Search API (#33822)

* feat: Add Perplexity Search API as web_search provider

* docs fixes

* domain_filter validation

* address comments

* provider-specific options in cache key

* add validation for unsupported date filters

* legacy fields

* unsupported_language guard

* cache key matches the request's precedence order

* conflicting_time_filters guard

* unsupported_country guard

* invalid_date_range guard

* pplx validate for ISO 639-1 format

* docs: add Perplexity Search API changelog entry

* unsupported_domain_filter guard

---------

Co-authored-by: Shadow <hi@shadowing.dev>

src/commands/configure.shared.ts

@@ -52,7 +52,7 @@ export const CONFIGURE_SECTION_OPTIONS: Array<{
 }> = [
   { value: "workspace", label: "Workspace", hint: "Set workspace + sessions" },
   { value: "model", label: "Model", hint: "Pick provider + credentials" },
-  { value: "web", label: "Web tools", hint: "Configure Brave search + fetch" },
+  { value: "web", label: "Web tools", hint: "Configure web search (Perplexity/Brave) + fetch" },
   { value: "gateway", label: "Gateway", hint: "Port, bind, auth, tailscale" },
   {
     value: "daemon",