I have a standard Google App Engine environment and am trying to serve some static files for my create-react-app frontend, but I’m not able to do so without copying over the client/build/ files into the server/ folder.

My file structure looks like this:

.
├── app.yaml
├── package-lock.json
├── package.json
├── tsconfig.json
├── client
│   ├── build/
│   ├── package-lock.json
│   ├── package.json
│   ├── public/
│   ├── src/
│   └── tsconfig.json
└── server
    ├── dist/
    ├── package-lock.json
    ├── package.json
    ├── src/
    └── tsconfig.json

What I had been doing is uploading all the source files to Google Cloud (and excluding the locally-built ones), letting it build everything in the cloud, and then at the end of the build process copying across the client files over to the server:
"build": "npm run build:client && npm run build:server && rsync -av --delete client/build/ server/build/"
but it seemed unnecessary to build files in the client and then copy them to the server.

I was thinking I’d use handlers in app.yaml to directly serve the static files from client/, based on the example here but also allowing my server to handle API requests. When I tried this, I added the following to app.yaml:

handlers:
  - url: /static
    static_dir: client/build/static

  - url: /(.*.(json|ico|js))$
    static_files: client/build/1
    upload: client/build/.*.(json|ico|js)$

  - url: /.*
    script: auto

and changed my routes in app.ts slightly:

// Routes
app.use('/auth', authRouter);
app.use('/api', apiRouter);
...

// Serve the React app
app.get('*', (req, res) => {
  res.sendFile(path.join(__dirname, '../../client/build', 'index.html')); // before it was just '../build' instead
});

but this meant that I got a 404 error whenever trying to access the frontend.

Is the correct approach simply to copy across the built files from client/ to server/? If so, is there a reason for this, and is it better to do it locally or as part of the build step in the cloud? Otherwise, what do I need to change about the handlers or routing for it to work?