Is web push supposed to work for linked devices?

[KareemJandali]

Hey, I'm hoping someone can tell me if I'm wasting my time here.

I'm calling RegisterForPushNotifications with a WebPushConfig from a
companion device (paired with a phone-number code). It always comes back
successful, no error. But I've never once received a push at my endpoint.

I've checked the obvious things: the endpoint is publicly reachable (I
tested it from outside right before and right after), the app is fully
force-quit so there's no socket open, and I log every request on every
path. Nothing shows up at all, not even a probe.

If I call GetServerPushNotificationConfig straight after registering, I
just get <settings webserverkey="..."/> back, with no endpoint in it.

Two things I can't figure out:

1. Is web push to linked devices still a thing, or has it quietly stopped
   working?
2. Does the endpoint have to be a real push service URL (something like
   https://fcm.googleapis.com/fcm/send/...), or can it be any HTTPS URL I
   control?

I noticed mautrix-whatsapp hardcodes the VAPID key, so it looks like this
is used in practice. I'm just trying to work out what I'm doing differently.

Thanks!