Welcome to the forums!! I hope someone can help you before you need to wait for a replacement. The satisfaction of troubleshooting is part of the fun. (Well, for some ;))
I mentioned this in another post, but check your pins. They are super tiny, and flexible. Sometimes two pins end up in one slot.
Try installing it all removed from the plastic housings. They don’t do it any favours re: cable alignment.
Re: the time and battery gauge, it only refreshes when it detects an input change. Since the keyboard isnt detected, that seems to line up.
As to why it’s always 4:07 on reboot. Hmm. Perhaps since it’s never experienced a reboot, this was the time it is by default. Very interesting!