I tried to change my Apple ID but I cant with the message "Continue on one of your devices"

This is not a recognized issue by Apple as far as I can tell. A preponderance of user reports say the solution is to use a browser other than Safari.

Related discussions:

https://discussions.apple.com/thread/255037783

- "Someone in another post said to use a different browser (not Safari or whichever one you normally use). That worked for me."

- "Use a computer to generate the App specific passwords. Don't use Safari or Chrome. I got it to work using Firefox on my Mac."

- "the Chrome browser works for me."

Can't change Apple ID - Apple Community

- "OK it just worked. No idea what was going on before. Thanks for the help anyway!"

Can't Change / Remove Apple ID Notificati… - Apple Community

- Occurred while changing account information using a web browser.

https://discussions.apple.com/thread/255040675

- "The solution to the problem is not to allow the iPhone or Mac to sign you in automatically with FaceID or TouchID, but instead I found complete success in manually signing in with my Apple ID and password, which then prompted a two-factor authentication prompt and code. Following that sequence, I was able to successfully revoke and add app-specific passwords."

I'm trying to add a new app-specific pass… - Apple Community

I was able to change mine by going through a Chrome browser rather than Safari

What worked for me was logging in to my AppleID manually. Then I was prompted for the two-factor authentication.