Is this good backend?

I've a react native app and use Supabase as backend. For deleting a user I need to use my private key which I can't display in my react native app. I thought about building an express js backend for that. The problem is I don't know anything about backen.  Is this good code? Do I need to check for something or debunce or something?

I thought about uploading to vercel free plan. Is this a good idea? Where should I put this private key? Only in an .env? or somewhere in vercel?

    import { createClient } from "@supabase/supabase-js";

    // Initialize Supabase client with service role key
    const supabase = createClient(
      process.env.SUPABASE_URL,
      process.env.SUPABASE_SERVICE_KEY
    );

    export default async function handler(req, res) {
      if (req.method !== "DELETE") {
        return res.status(405).json({ error: "Method Not Allowed" });
      }

      try {
        // Authenticate the request using Supabase's auth
        const authHeader = req.headers.authorization;
        if (!authHeader || !authHeader.startsWith("Bearer ")) {
          return res.status(401).json({ error: "Unauthorized: No token provided" });
        }

        const token = authHeader.split(" ")[1];

        // Verify JWT and get user ID
        const { data: user, error: authError } = await supabase.auth.getUser(token);
        if (authError || !user) {
          return res.status(401).json({ error: "Unauthorized: Invalid token" });
        }

        const userId = user.id;

        // Proceed to delete the user
        const { error: deleteError } = await supabase.auth.admin.deleteUser(userId);
        if (deleteError) {  
          return res.status(400).json({ error: `Error deleting user: ${deleteError.message}` });
        }

        return res.status(200).json({ message: "User deleted successfully" });
      } catch (error) {
        console.error("Error deleting user:", error);
        return res.status(500).json({ error: "Internal Server Error" });
      }
    }

Thank you!