Switching monitors between two machines

Hello! I'm in a situation, where I have a work laptop and a personal computer, the latter is used mostly for gaming. In order to switch between them I have to plug all the peripherals from one machine to the other, to help with that I bought a dock, to which I can connect everything, and connect the dock via one USB-C cable. The trouble begins with the monitors, as my laptop supports thunderbolt, but my motherboard doesn't, so it's a bit of a chore to switch them.

To alleviate the issue I'm considering changing my motherboard to one that has thunderbolt 4 support, as I have one 4K monitor and one full HD, and I've read it should support them fine on one cable. Is this a good solution? I'm thinking I might run into some issues with monitors not being connected directly to my GPU, latency or otherwise.

I beseech thee for help o masters of the PC.