I have had similar issues with the same device it's been somewhat intermittent but from time to time the device would be sitting with the screen off and be warm to the touch. Draining the battery a significant amount usually closing apps doesn't really seem to help (maybe slightly) however a reboot each time would solve it.
At first i thought it might have something to do with how the device interacts with Google cast devices on the local network but was not able to replicate anything firm around that. Then i thought perhaps it was Home Assistant polling often so i disabled that app. Still continued to have the same issues.
Checking the output on top on the phone through ADB i could see that when in one of these drain states the system_server process was consuming the most CPU along with com.google.android.gms.persistent. Killing the gms process reduced CPU but the system_server remained unchanged.
Processes During Battery Drain: https://imgur.com/a/hLiE0In
Restarting the phone and checking the running processes again the utilisation is much lower.
Processes After Reboot: https://imgur.com/a/A00XXBa
I noticed after not being connected to WiFi for a while that the battery drain is suddenly not an issue and battery life is much improved. For the time being i'm going to remain using mobile data only to see if i encounter the same issues if i don't that at least narrows it down a bit. Checking now with the phone WiFi the CPU usage appears to be even lower.
Processes on Mobile Data, WiFi Off: https://imgur.com/a/XsDydQo
Taking a look in the data usage of the phone it appears on WiFi that "Android OS" says it has used a total of 369GB which is just absurd. I'm not sure exactly how that's calculated and if that's normal or not, my old device has 180 GB for the same time period which is the 16 Oct to 13 Nov but the Pixel 9 Pro I've only had since the start of the month, something is very strange there i haven't done any large data transfers.
I'll keep monitoring things without WiFi and then all going well start trying to narrow down if an app causes the system_server process to go crazy or if there is some other way this can be replicated.