Hey DownTimeTech,
It sounds like you're having trouble entering your Apple ID password because it closes and reverts to the Home screen.
As a first step, be sure to restart both the iPhone and the Apple Watch:
Restart your iPhone
How to restart your Apple Watch
If that doesn't help, also try updating:
Update your Apple Watch
If it's still closing the log-in screen, try unpairing the Apple Watch and setting it up again. When you unpair, the data will be erased from your Apple Watch but a backup is also created when unpairing. You can still make a manual backup using these steps: Back up your Apple Watch
When you're ready, use these steps to unpair the Apple Watch and set it up again: Unpair and erase your Apple Watch. Then pair and set it up again: Set up your Apple Watch
Keep us updated. Cheers!