Hey there, AndyDemens!
We see you're having some trouble with your apps running in the background; we'll be more than happy to look into this with you.
You stated that you don't have the Twitter app on your iPhone. Did you ever at one point have that app on your iPhone? Do you have any other iOS devices that may have the Twitter app installed on it? If so, do you have "Share Across Devices" turned on in Settings > Screen Time?
Use Screen Time on your iPhone, iPad, or iPod touch
If you did at one point download Twitter to this specific device let's check to see if it may be hidden somewhere. We can search for that app, then remove it once it is found: Use Search on your iPhone, iPad, or iPod touch
You can also see if it is authorized to run in the background by checking your Background App Refresh. This can be found under Settings > General > Background App Refresh.
Let us know what you find.
All the best.