How can you check the passwords on the Thunderbird phone app

This is the Thunderbird for desktop devices forum. You would be best off asking your question in the Thunderbird for Android forum where its experts hang out:

https://support.mozilla.org/en-US/questions/mobile

The account password can be found on the below setting pages.

• Settings > account name > fetching mail > incoming server
• Settings > account name > sending mail > outgoing server

This assumes normal password authentication is being used. You won't see a password field on these pages for oAuth 2.0 authentication.