Hi Katharine Crouan !
Re: "Problem entering Apple ID on Apple Watch SE: watch keeps prompting me to enter my Apple ID on ‘settings’."
"drawing each letter and numeral in the designated space"
If the wrong case appears when you enter a letter
try turning the digital crown to select upper or lower case (or predictive text etc.)
or
If your paired iPhone is nearby, see if a notification appears on the iPhone, offering to let you enter text using the iOS keyboard. Tap the notification, then type the text using the iPhone keyboard.
or
See if you can sign in from the Apple Watch app: Tap General > Apple ID, then sign in.
Else Apple support's online articles may be helpful:
Tips on how to use : Scribble on your Apple Watch - Apple Support
You could also check if your Apple ID may already be listed:
Manage your Apple ID settings on Apple Watch - Apple Support
says: Manage Apple ID password and security
- Open the Settings app
on your Apple Watch. - Tap [your name], then tap Sign-In & Security.
- The phone numbers and email addresses associated with your Apple ID are listed, along with their status—for example, Primary or Verified. (To make any changes: see the above article for tips)
Hope something here works for you :-)