A:Answer I can't speak for that particular player, but this projector does accept a native 4K HDR signal from my PS4 Pro, XBox One S, and Fire TV (box, haven't tried the stick).
Also be advised that only one of the HDMI inputs (I believe HDMI 2) supports HDCP 2.2, so you'll need to use some sort of switch for multiple devices. If you're considering this projector and use your audio receiver as a switch for HDMI, remember to check if your receiver supports 4K/HDR passthrough with HDCP 2.2. Otherwise, you'll probably have to get a compatible HDMI switch (I'm currently using the SwitchDeck SW-32911) and run an optical cable back to your receiver for audio.