To swap keyboards, mouse, headphones DAC and Microphone from Laptop to Desktop and vice versa, I have an iogear USB switch (https://www.iogear.com/product/GUS432/
- it's not that expensive any more). As for the monitors, I have my desktop connected directly to them, and for the laptop you could have a USB-C DisplayLink dock. You could connect the USB Switch to the DisplayLink dock to have a "one cable" solution.
It's not a one button switch solution, but it's a very reliable one imho.
Just a caveat, for the usb switch to work with more devices, you will need an actively powered USB hub connected to the switch, as it will not provide enough power.