feat(search): add Antigravity as a web search provider

Route POST /v1/search with provider "antigravity" through Google Search
grounding on v1internal:generateContent, using the existing Antigravity
OAuth account pool. Grounding chunks become citations with the grounded
sentence as snippet and its surrounding answer text as content.

Upstream repeats a source across chunks, so citations are keyed by URL
and their snippets merged. A missing projectId is reported up front —
upstream answers a fabricated or absent project with a misleading
"no valid license" 403.

Based on the approach in #3437 by @Nautilaceae.

open-sse/providers/registry/antigravity.js

@@ -17,7 +17,7 @@ export default {
     deprecationNotice: "RISK_NOTICE",
   },
   category: "oauth",
-  serviceKinds: ["llm", "image"],
+  serviceKinds: ["llm", "image", "webSearch"],
   transport: {
     baseUrls: [ANTIGRAVITY_IDE_BASE_URL],
     format: "antigravity",
@@ -82,6 +82,11 @@ export default {
     loadCodeAssistUserAgent: ANTIGRAVITY_IDE_USER_AGENT,
     refreshLeadMs: 300000,
   },
+  searchViaChat: {
+    defaultModel: "gemini-2.5-flash",
+    endpoint: `${ANTIGRAVITY_IDE_BASE_URL}/v1internal:generateContent`,
+    freeTier: "Free — Google Search grounding through an Antigravity OAuth account.",
+  },
   features: {
     usage: true,
   },