Hi, apologies for yet another clueless post, but these things are hard for some 
I have two computers, that can only output HDMI video. I have two screens that can take HDMI input. I have one USB keyboard, one USB mouse and one USB headset.
I need one computer to have both screens connected and one to only connect to one.
The peripherals need to be shared (obviously).
Is this even possible? And in case it is, which KVM do I need?
Most screens have two inputs, so I would simply use that. Sure, you need to press a button to change inputs when you want to use the other computer, but other than that, you can use any KVM switch to accomplish the same thing.
Or, depending on how important latency is to you, you could just get one of these puppies that allows you to RDC to the other computer over network, something like this:
Two solutions that achieve what you want for a low cost. You are welcome.
Thank you for a quick reply!
I have a question though. In case i use the second input port on one of the screens for the 2nd computer (i checked, it has one ), I would also have to unplug both the USB keyboard and the USB mouse (and the headphones) from one computer and plug them into the other one, if there is no KVM involved, correct? (this is what I am trying to avoid, tbh)
If you only have 2 PCs and one of your monitor has 2 HDMI inputs, the easiest fix is to add a USB 2-port switch (and maybe a USB hub if the switch only has 1 port) to the mix. But you’ll have to live with the horrible, horrible need to press 2 buttons instead of just 1 (on your monitor and on the usb switch). Oh, the travesty!
Note that most monitors (and at least the L1 DP KVM 4 PC 1 monitor I own) don’t have a built-in fake display emulation, meaning that the button on the monitor (and the KVM) will basically “physically disconnect” the port from one PC and connect the other port to the next.
This is for performance reasons, as emulating / cloning a fake display introduces latency. That makes for the unfortunate behavior of your PC with 2 monitors to detect the disconnection of the monitor and readjust your windows (not a big deal if you use something like sway on linux 
). Well, same goes for the PC with just 1 monitor, it’ll see you have no monitor (when you’re using 2 monitors on your other PC) and might misbehave.
There is a L1 KVM that has full display emulation (the Thin Clients version). There’s also the L1 DP repeater, but idk if they have an HDMI version.
Some monitors come with a full emulation too and basically when you switch the monitor input, the PCs won’t even know that the output changed, yours might have it, so check that out before buying something as expensive as a KVM.
Unless your needs are very limited, I don’t recommend anything other than L1 stuff, but if you only need a dumb 1080p KVM, you can buy the cheaper alternatives.
For right now, I still suggest you get a USB switch and use the monitor’s input switch along with this.
Yes, that (a rudimentary USB 2-port switch) makes the most sense. Thank you for the suggestion. And I hope my therapist will be able to deal with the aftermath of the dual-button-pushing thing 