refactor: migrate deprecated middleware convention to proxy (Next 16)

Middlewate file convention is deprecated in Next 16.3.5 (renamed to proxy).
git mv middleware.ts -> proxy.ts, rename exported fn middleware -> proxy.
Build now emits `ƒ Proxy (Middleware)` with no deprecation warning.

proxy.ts

@@ -0,0 +1,23 @@
+import { NextResponse, type NextRequest } from "next/server";
+import { getSessionCookie } from "better-auth/cookies";
+
+const PROTECTED_PATHS = ["/protected"];
+
+export function proxy(request: NextRequest) {
+  const { pathname } = request.nextUrl;
+
+  if (PROTECTED_PATHS.some((p) => pathname.startsWith(p))) {
+    const sessionCookie = getSessionCookie(request);
+    if (!sessionCookie) {
+      const loginUrl = new URL("/", request.url);
+      loginUrl.searchParams.set("next", pathname);
+      return NextResponse.redirect(loginUrl);
+    }
+  }
+
+  return NextResponse.next();
+}
+
+export const config = {
+  matcher: ["/((?!_next/static|_next/image|favicon.ico|api|.*\\..*).*)"],
+};