The problem is, the usual solution for cheap KVM doesn't give you power delivery from the monitor, you will need a separate USB C PD power supply. And yet, that's the best I can suggest.

If USB 2.0 data is enough this $13 USB C adapter which has a DisplayPort output and a USB data port and power passthrough can be recommended.

You will also need a USB switch and run https://github.com/haimgel/display-switch on all three so the monitor switches inputs as the USB switches.

You will likely need a bidirectional USB C - DP cable because AFAIK the monitor only has three inputs so you need to use the C port by connecting one of the DP outputs to the monitor C input. You will also likely need to buy a C-B cable because the little doohickey only has a C data port and most switches have B inputs and they only ship with A-B cables.