Note: as of February. 9, 2025, the latest version seems to be 7.12.1 released Feb. 2, 2025.
In my case, the problem I was having is that the old version was indeed still on the app server). I was deleting the old app and reinstalling, but I was going through through my "purchased" or "not on this device" areas. In those cases, it downloaded the older version of the app that didn't work.
I deleted the app from my Apple TV, but this time I went into the Apple App Store and searched for the SiriusXM app. Only one app appeared, and it was the new version 7.12.1. I downloaded it, opened the app, and used the QR code it displayed on screen to get to the web page for signing in. It already had the correct code entered. After continuing, I entered my streaming credentials (which are different from my main account login for the website). It activated the new app, and I've been streaming for an hour without it stopping. It seems that corrected the problem.
Not sure why SiriusXM would leave the older versions up there. Maybe for older devices that don't have or can't install the latest TVOS version? Anyway, Thanks to the posters who helped sort this out!