fix: add variant diagnostics to health endpoint and lite mode banner

Users running lite mode had no way to tell why AI tools were greyed out.
Now the public health endpoint reports the variant, and a visible banner
appears in the tool panel when running in lite mode.

apps/api/src/index.ts

@@ -112,6 +112,7 @@ await docsRoutes(app);
 app.get("/api/v1/health", async () => ({
   status: "healthy",
   version: APP_VERSION,
+  variant: process.env.STIRLING_VARIANT === "lite" ? "lite" : "full",
 }));
 
 // Admin health check (full diagnostics)