This week, Google gave us the ability to roll back problematic Play system updates right on our devices through Mainline services (found in Google system services). Since my S23 Ultra has been stuck on the July update, I decided to see if I could roll back and force a current Play system update. Doesn't look like it:
Found under settings > Google > all services > system services
I see this incompatibility message on my S23U and Tab S9, both of which have been updated to One UI 8/Android 16. I do have the "remove updates" option on my OnePlus 13, which is still on Android 15. This message, as well as the numerous complaints from other users about this issue, leads me to believe that there's a systemic problem with Google Play system updates on at least Samsung devices running One UI 8 (possibly other OEMs' devices running Android 16).
It doesn't look like users can do anything except wait for a fix from Google, which doesn't seem to be coming anytime soon. If community moderators are able to raise this issue up the flagpole, it would be much appreciated. Meanwhile, I may try to use the Google Play System Update Rollbacks (GPSUR) tool through ADB. I'll report back if I have any success.
Device Health Services still runs in the background. Device care is completely different from Device Health Services. Samsung just removed the user interface for battery health monitoring. Device Health Services just runs in the background and doesn't really do much. 
There's a battery health section, but I don't think it's the same as on Pixel. You can see that I can choose between either smart charging or setting a custom charge limit. 
