Hello Skkibunni,
It sounds as though you're signing in to a third-party app on your iPhone and upon signing in, that change is also happening on another device. You've walked through great steps thus far and have come to a wonderful place for help.
There is the possibility that you may need to contact the application developer for support, but before it leads there try the steps listed below. You can also find these steps in the following article.
"Force the app to close. Then open the app to see if it works as expected.Restart your iPhone or restart your iPad. Then open the app to see if it works as expected.To see if updates are available for the app, open the App Store, tap your profile icon, then scroll down to see if updates are available. If updates aren't available for the app, update the software on your iPhone or iPad. Delete the app. When you do this, you might lose data that was stored in the app. Then redownload the app. Then check to see if the problem with the app is fixed."
If an app on your iPhone or iPad stops responding, closes unexpectedly, or won’t open
While the title of that article outlines different issues, these steps can be helpful in resolving the issue you're facing. If you continue to have issues with the app signing in to the same account on the other device, reaching out to the application developer is the right next step. Their contact details can be found using the steps in the article below.
How to contact an app developer
Have a great rest of your week!