What problem is this issue looking to solve?

The service worker passes requests to .php files to the web worker. However, the web worker may not be loaded yet or it could be busy at the moment.

How does this issue proposes to solve it?

Reply with HTTP 502 or HTTP 408 eventually somewhere here:

https://github.com/adamziel/wordpress-wasm/blob/9d04a113a97f53a1303fefba642f65f1b5a5a5f6/src/web/service-worker.js#L31-L52