Sadly there’s no (official) way for PS5 remote play on PS VITA.

I’m charging my phone every night due to Sleep as Android, so battery drain isn’t really a thing I’m looking after. But you are absolutely right here.

As already suggested you might take a look at IFTT.

Isn’t that the default behaviour? I never switch manually, but always use WiFi at home and mobile data when I’m out.

WiFi and mobile data are activated all the time.

Samsung Galaxy S10 Android 12

Care to share the link for the Chibi Cthulhu?