I tested the Muon 404 and was able to get a lock using the particle-som-gnss library on battery only.
The battery should charge in 4 hours off 12 VDC input.
The battery should also charge off USB-C, but only from a real USB-C port. If you are using a USB-A to USB-C cable, the USB port won't switch to 9V and the battery will not charge, and the Muon won't run (except off battery).