Twidere is a very nice F/LOSS Twitter client available through FDroid:
Trying to login to Twitter with it gives “Incorrect API Settings” message
Remove the account. Somehow you’ll get to an Advanced > Network > API settings screen that has a Load Defaults button. Tap it. When it’s finished, go to Accounts and add your account back.
How to log out of Twitter from Twidhere?
Remove the account. Not at all intuitive, but that’s how it works.