Interesting, it feels a bit over engineered but it might work.

I'm not sure about the efficiency thought, websockets needs a costant live connection, serverless functions are throwaway instead.

On execution they would stay alive until their time limit (15 seconds it seems) and do what they can by taking to the DB, then they dies and the client have to connect to a new one.

The use of serverless functions is for small activities that need a one-time action, that setup will cost a lot.

What I can think for a serverless use is a shared backend for smaller relays, like something to trigger on certain events.