I'm having the same issue after update to iOS 17. Play counts are not updating on other devices from iphone or ipod touch.
At the moment, itunes music doesn't seem to recognise that I'm using it on multiple devices. In the past, if I tried to play music on my iphone (for instance) while music was already playing on another device, I would get a warning message and music would stop playing on one of the devices.
However, this morning I tried playing music simultaneously on four devices (iMac, iphone, ipod touch and apple music on a PC) and had no messages and music kept playing on all devices at the same time.
I wondered if my apple ID was not working properly, but checked and I seem to be properly logged-in on all devices.
Furthermore, If I add a new album on one of my devices (all four), it appears on all my devices (all four), so apple ID is presumably fine. And if I manually update the music library on my Mac or PC (file/library/update icloud music library) the libraries update properly on my phone and ipod (and MAC/PC).
It just seems to be the play counts that don't update properly to icloud from my iphone or ipod. Up to installing iOS 17, the play counts updated automatically at least once a day, usually after the first play on iphone/ipod. So far, neither the plays from iphone or ipod have synced for two days.
I tried un-toggling the "Sync Library" on my iphone and then turning the "Sync Library" on again, hoping this might force a fresh sync. But it didn't.
I installed another update this morning that claimed to solve some bugs (icloud music problems was not listed as one of the issues), but, so far, there is no evidence that this update has helped.
One thing I did note this morning while looking at icloud settings on my phone, was that it asked me to agree to new terms and conditions for icloud. Again, no evidence yet that this has helped solve the play count issue.