Basically what the subgenre l subject says.
I have a librem mini, first gen. And the one thing I miss on it is that the usb-c is just that and not thunderbolt. So it can take the mouse and keyboard from my KVM but not the screen.
I’d like to either replace our add a thunderbolt but have no clue whether that’s possible.
no, it’s not possible. On 10th-gen and earlier platforms, TB requires a separate chip to implement, and since that is not on the mainboard, there is no way to add TB to the LM. On a desktop board with PCIe slots you could do it via an add-on card, but via a mini-PC there’s no way to do so (to my knowledge)
Yes, this can be an annoying juggle.
Is a workaround that your monitor has multiple video inputs so that you can connect the Librem Mini direct to the monitor, bypassing the KVM switch? Then you might have to switch the keyboard and mouse via the KVM switch and the video manually using the monitor’s own controls.
Is a suitable external adapter available? (However in my experience plugging a whole lot of hardware together like that can be hit and miss.)
This is indeed what I do now, but it’s sub optimal for my current setup and way of working.
But I guess I’ll just have to deal with it
That’s what I feared and thought as well. Sad side effect of using a mini I guess.
“This” being? Which option?
Assuming you mean “bypass the KVM switch”, LOL yes it’s what I do now too (completely different hardware involved but same problem).
What’s the native resolution of your monitor?
PS
Regardless of Thunderbolt, the USB-C port on the Librem Mini does not support video output over USB-C. So there are two separate but possibly related issues.
I don’t think any Purism hardware supports Thunderbolt (out of the box) but at least the Librem 14 and the Librem 5 can both do video output over USB-C.
The bypass indeed, sorry, answering from mobile phone is somewhat crap, didn’t see I did not quote.
The resolution is a simple 1920 x 1080 which suits me fine for now. Was mainly curious if it indeed is complex to make the KVM work properly with both machines I use 
Then an option may be to use an adapter to convert video over Thunderbolt to either DisplayPort or HDMI on the other device, then use the DisplayPort or HDMI port respectively on the Librem Mini, and finally use a KVM switch that switches the appropriate type of video (whichever you have chosen, DisplayPort or HDMI).
(I guess I should have asked the frame rate too. So I am assuming that with FHD - 1920x1080 - and a modest frame rate, any video standard will be adequate, any adapter could work, any KVM switch could work.)
But, at FHD resolution, it might be cheaper to buy another monitor if your setup has the space.