Google stores an app password in your email client, not your actual password. When you change your password, Thunderbird needs to receive the updated password. I suggest clicking to settings>privacy&security to delete the current password and then pursue getting the new one. After you respond to the Google prompt, Google will store a new app password in thunderbird.

Google is asking for 2-step verification but is not allowing me to use the simplest of verification - a text message. That option is grayed out.

Google are offering multiple ways to sign in. Go to your Google account and select Security - How you sign in to Google. https://myaccount.google.com/

Pick the method which fits best for you.

Can I make changes directly in Thunderbird and this imap and avoid this Google nonsense?

No, you can't. And it isn't nonsense, it's in you best interest.