Why won't my PS4 Pro work with any 4K HDMI switch?

looks like you need a mechanical switch for your splitter, or your switches don't have HDCP, I quote description from your second switch :

ULTRA HD RESOLUTION - This 4K HDMI Switch supports resolution up to 4K@30Hz, 1080p 3D@60Hz, 1080p Full HD@120Hz. HDMI version 1.4 and backwards compatible (NOTE: It CAN'T compatible with HDCP 2.2)

The ps4 pro doesn't run on 4K@30Hz, & it needs HDCP... AND you want HDMI 2.0 minimum.

So something akin to this might be your solution (checkout the product description for more info).

Good luck !