Good luck, I haven't been able to find an HDMI switch compatible with a PS4 Pro (tried 3 different switches all claiming to be compatible).
I've been using this with no issues at all.
HUIERAV HDMI 2.0 Ultra HD 4Kx2K/60Hz HDMI Switch| HDMI 2 Ports Bi-direction Manual Switch 2x1 or 1x2 AB Switch Splitter https://www.amazon.co.uk/dp/B06VVM9312/ref=cm_sw_r_cp_apa_X41rAb7ANH9J0
It works splitting the output from the pro to the TV and psvr and also the other way doing two outputs into one input.
The customer service is excellent too as my first unit had a handshake issue on output 2 and they just sent another out for free without asking for the original unit sending back