Hi Millerr210,
Thanks for using Apple Support Communities! We see you're having trouble with entering your Apple ID password on your Apple Watch, and we'd like to help.
Testing the # character in the Messages app, and it does populate using Scribble.
Send messages from Apple Watch
However, if you aren't able to get that to populate, you can use the Apple Watch app on your paired iPhone to enter in your Apple ID password. This information is included in Step 5 of the article viewed before posting:
Set up your Apple Watch
This article can be helpful, since you mentioned new iPhone:
How to pair your Apple Watch with a new iPhone
Take care!