Having plugged the controller in using multiple different cables, adapters and sockets for well over 10 hours at this point, I've concluded it will no longer charge. It works whilst connected via a cable, but that somewhat defeats the point.
I have a founders edition, so I'm wondering how to have it replaced under warranty.
@MichaelHS Sorry to hear that. Have you tried resetting the controller to see if that might help at all? It's possible that will re-initialize the charging circuitry and get you back up and running.
If not, you'll want to contact Stadia support to see about opening a warranty claim: