Say I send a message to someone who has a phone with push notifications enabled, showing message previews. Will the phone still be connected to the VPN when it wakes up to display the message? Because my iPhone doesn't seem to stay connected to my VPN when it sleeps, at least not reliably.

There really should be a "never use the internet without VPN" mode on devices.

That exists on Android. VPN on ios is known to be rather leaky.

Valid point. Afaict, vpns I've used route all network activity regardless of phone state, but that's likely dependant on the service.

I don't see how that can work for the push packet itself, cause I thought that's specially handled by some low-power hardware on the phone while the main parts are shut off. Unless that hardware is also managing the VPN connection, which I doubt.

So if there's no always-on hardware maintaining that VPN connection, probably the phone is going to wake up without it. And even if it auto-reconnects, it'll probably load stuff before it's connected to the VPN.

Yeah, probably only if mobile data is turned off so the packet doesn't hit the mobile network, and only wifi calling /messaging could the VPN hide location.