your post doesn't make much sense.
the video capture device is connected to your PC via USB-C,
to the PS4 via HDMI,
and then outputting to a display via HDMI?
what are trying to use the splitter for?
are you trying to split the video capture device's output to two different screens?
many of the available video cable splitters, converters, hubs, etc out there on the market are very unreliable.
most manufactured with low quality components and cannot handle the bandwidth needed to operate at their reported specs.
any you would like to use you should make sure that you find multiple customer reviews with others acknowledging that it can actually handle what you're looking to do.
and even if they do, malfunctioned and DOA products are fairly more common these days than in the past.