feat: shared login with session cookie

app/api/auth/logout/route.ts

@@ -0,0 +1,14 @@
+import { NextResponse } from "next/server";
+import { SESSION_COOKIE } from "../../../../lib/auth";
+
+export async function POST() {
+  const res = NextResponse.json({ ok: true });
+  res.cookies.set(SESSION_COOKIE, "", { path: "/", maxAge: 0 });
+  return res;
+}
+
+export async function GET(req: Request) {
+  const res = NextResponse.redirect(new URL("/login", req.url));
+  res.cookies.set(SESSION_COOKIE, "", { path: "/", maxAge: 0 });
+  return res;
+}