I need niche KVM hardware advice

I have a 2 monitor setup on a monitor arm. Both have 1 HDMI and 1 DP input. One of them also has a USB-C input. I need something that allows me to switch easily between either 1 or 2 laptops or a destktop input.

To be clear, the scenarios I want to switch between are:
- The desktop driving both monitors
- Each laptop driving one monitor + their laptop monitor, one at-, or at the same time.

(Being able to have one laptop driving both displays when only one laptop is present is a nice to have, but definitely not a must.)

I already have 2 of those HP thunderbolt docs, so I can connect the laptops with a single cable to those, and then from there to the KVM.

What I want is a super relaible way to switch between laptops and the desktop, connect and disconnect a laptop here or there and have it drive the expected displays quickly without having to mess around with lot's of cables, or the OSD's.

Can anyone recommend a decent KVM that can do this? (Bonus points if it cost <€200. 😅)

Thanks Reddit!