Dunno what your actual issue is. If it is the downgrade from 4k to 1080p a splitter won't work (even if it's a 4k rated one).
The PS4Pro will always detect the lowest resolution in the chain. If you were using a 1080p splitter, it would be the splitter. A 4k splitter will just move that down to the Elgato.
If you want to plug in both the Elgato at 1080p and a 4k monitor/TV and get the right resolution, you need an active downscaler.
I THINK something like this may work:
No experience with the product btw. So purchase and use if you can return it if you can't use it. It may introduce some lag as well, as there is additional post processing going on. I don't know if that applies to outputs at native resolution or just outputs actually getting downscaled, in which case it wouldn't matter.
You’d need a scaler: https://www.amazon.com/dp/B079HN327D/ref=cm_sw_r_cp_apa_i_oFp.AbG6DQ55G
Either that, or pick up a different vendor’s capture cards that have a built-in scaler and 4K passthrough. https://www.razer.com/gaming-broadcaster/razer-ripsaw-hd
gofanco Prophecy Intelligent 4K 60HZ HDR 1x4 HDMI 2.0 Splitter - 4:4:4, 3D, HDMI 2.0a, HDCP 2.2, EDID, 18Gbps, Auto Scaling, Low Heat, Cascadable, Firmware Upgradable, 4 port 1 in 4 out https://www.amazon.com/dp/B079HN327D/ref=cm_sw_r_cp_apa_i_oFp.AbG6DQ55G