Here’s the support page:

help.steampowered.com/en/…/33E8-5EDF-24E6-4CFB

Flashing red should mean that the controller is in software update mode, trying to connect. I’d recommend restarting steam (or steamOS), and then plugging the controller straight into the usb C cable while it’s still off. If that doesn’t work, then you’ll probably just need to wait for Steam to get back in touch with you.

If steam support provides a button combination to reset the controller or something similar, please share it.