Using an HDMI splitter with two computers and a KVM switch

I'm trying to figure out if what I'm picturing in my head is really possible.

What I have is two computers, a Dell Latitude 5400 and a 2023 Mac mini with M2 Pro. I have dual 24" Dell monitors I want to share between the computers at the flip of a switch. I bought the Sabrent USB Type C Dual KVM Switch because it advertised being able to do this for both computers. Since this switch has two HDMI outputs, I connected those to my two monitors. And for the two inputs on the switch, I used a USB-C cable for both the laptop and Mac mini. When I switch to the laptop, it works perfectly, allowing me to extend the display to the two monitors, and using the laptop screen as a 3rd. But the Mac mini only sees a single monitor, even though both monitors are on, but they are mirrored. I now know this is because the Mac mini does not support MST. It's not the end of the world, I mainly needed the dual monitor support for the laptop. But I'm still trying to make it work for my Mac mini, so, here's what I'm thinking.

I still have the HDMI slot on my Mac mini opened, and I know the Mac mini can support up to three monitors. I'm wondering if I can use an HDMI splitter to take the HDMI cable out of one of the two monitors I have and put it into the input of the HDMI splitter, then the two outputs would go to that monitor and my Mac mini, and I'm wondering if when I use the switch the same way I'm using it now, will that second monitor properly switch between both computers.

I'm hoping someone here can let me know if this is possible how I've described, or if I need to do something different, or if this is not possible at all.