Well I downloaded something called Ampere which monitors the battery charge/discharge rate. I observed it's discharge rate (screen and CPU mostly, presumably), then plugged it into various chargers and cables.
It would appear it has a limit of about 1.1 amps going into the phone's USB socket. The battery will charge at at least 750mA, maybe more, I can't observe the current with the screen off or the phone powered down. It's a 3.3Ah battery. But if I max out the 8 core CPU, the battery just charges slower, totalling the same 1.1 amps input. This is plugged into a USB 3.2 rev 2 socket on my computer which should mean 1.5 amps available. If I use a 1 amp charger, it drops slightly to 1 amp. If I use a 500mA charger, it drops to 500mA. Not sure how it does that since I was using a charging cable, which has no data lines to communicate the allowed current. Maybe the chargers just drop the voltage automatically or because of internal resistance?