I only ever really noticed the cursor issue in GT Sport as well, and it was after an game update. Both of my two issues were after updates, although my second issue was after a console update.Both my wheel base and rim are already on the latest firmware. It's really weird how most of these issues only crops up in GTS though. Like the random button presses earlier, and the cursor drift. If I'm playing on PC I don't get it at all (or very very rarely). It's almost like GTS is just too sensitive to inputs. This week it's been behaving though *touch wood*.
I use a Ricmotech adapter to connect my old G25 pedals to the T-GT and with GTS I also get lots of throttle flickering (bless the pots, they are near 12 years old now). A few sprays of contact cleaner usually cures it, but within a week it returns. But when I'm playing on Assetto on PC, it's perfect stable throttle input, no flickers at all.