Fix infinite redirect on /studio by serving index.html directly

[...path] catches /studio itself (empty rest param), causing a redirect
loop. Now reads and returns index.html content for all /studio/* paths;
static assets are still served before this route fires.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/pages/studio/[...path].ts

@@ -1,7 +1,21 @@
 import type { APIRoute } from "astro";
+import { readFileSync, existsSync } from "fs";
+import { join } from "path";
 
-// Redirect deep studio links (e.g. /studio/desk/post) back to /studio so the
-// SPA can boot and handle its own routing. Static assets under /studio/assets/*
-// are served before this route ever fires.
-export const GET: APIRoute = () =>
-  new Response(null, { status: 302, headers: { Location: "/studio" } });
+// Serve the studio SPA for all /studio/* paths (including /studio itself).
+// Static assets under /studio/assets/* are served before this route fires.
+export const GET: APIRoute = () => {
+  const indexPath = join(process.cwd(), "dist/client/studio/index.html");
+
+  if (!existsSync(indexPath)) {
+    return new Response(
+      "<p>Sanity Studio has not been built. Check the Docker build logs.</p>",
+      { status: 503, headers: { "Content-Type": "text/html" } }
+    );
+  }
+
+  return new Response(readFileSync(indexPath, "utf-8"), {
+    status: 200,
+    headers: { "Content-Type": "text/html; charset=utf-8" },
+  });
+};