When launching the PS5 version of the game, my girlfriend and I experience the same drifting issue where our characters and cursors within menus will constantly drift downward.
We started just playing the ps4 version of the game to get around it, as the drifting prevented item inspection most of the time because the stat windows apparently require the cursor to remain stationary on the items.
I’m fairly certain that it’s not the controller, as we do not experience the drifting with any other PS5 games and these controllers are different iterations of distribution (Hers came with the system, mine is the red and black version that was was released later).
Try lowering the sensitivite in the gameplay options.
Isn’t that cursor sensitivity? That would only make it drift slower, I would assume.
Just a tought, worth a try atleast 
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I do appreciate the suggestion, after the ~7 hour “Character With That Name Already Exists” lockout that I had yesterday and the fact that people are reporting it again today, I’m not sure if it’s worth the risk of bouncing clients atm. I’ll have to test it when that issue goes away.
It does look like other people are seeing the same issue, based off of web searches. Imagine that it’s just a lot smaller pool of people with this issue. I just hadn’t seen that anyone had submitted anything for it, so just trying to make sure that it is known (I’m sure it is). Thanks!
I have the exact same issue and have reported it. Not an issue with the controller itself, as it only happens in Diablo 2: Resurrected. Player character and menu cursor drift downwards on their own. Feels like the deadzone is too sensitive or too low. Settings for this in-game would surely resolve the issue completely?
I can verify that I have the exact same issue of downward drift on both my PS5 controllers. Only happens in D2R (when I can actually get into a game).