feat: add Chrome extension browser relay

src/browser/routes/basic.ts

@@ -111,6 +111,9 @@ export function registerBrowserBasicRoutes(app: express.Express, ctx: BrowserRou
     const name = toStringOrEmpty((req.body as { name?: unknown })?.name);
     const color = toStringOrEmpty((req.body as { color?: unknown })?.color);
     const cdpUrl = toStringOrEmpty((req.body as { cdpUrl?: unknown })?.cdpUrl);
+    const driver = toStringOrEmpty(
+      (req.body as { driver?: unknown })?.driver,
+    ) as "clawd" | "extension" | "";
 
     if (!name) return jsonError(res, 400, "name is required");
 
@@ -120,6 +123,7 @@ export function registerBrowserBasicRoutes(app: express.Express, ctx: BrowserRou
         name,
         color: color || undefined,
         cdpUrl: cdpUrl || undefined,
+        driver: driver === "extension" ? "extension" : undefined,
       });
       res.json(result);
     } catch (err) {