I'm searching for a USB-C (not USB-A) switch. But does such a device even exist?

Question

TL;DR : I'm trying to find a way to share a USB-C connection with at least 2 sources, like a switch or a KVM. But I only found USB-A switches so far.

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I'm struggling to find the appropriate hardware for my problem.

I have a triple display setup connected to my work laptop (and sometimes my own personnal computer) through a docking station (D6000 from DELL).

But I'd like to avoid unplugging and plugging back the docking station to avoid as much cable management as I can. So I tried adding a USB-3 switch (USB-A, this one), but it look like going through USB-A makes triple display non-functionnal (1 of my monitors doesn't work that way, confirmed by the manual).

So, I'm trying to find an equivalent, but full USB-C (Switching an USB-C stream through different sources, like pushing a button would change the selected USB-C source but to an USB-C output), yet so far I have found none. I have searched on several websites (Startech constructor website, amazon, several search engines...), but so far I failed to find one.

Any hardware recommendation that would meet my requirements ?

Desired setup :

Monitor    Monitor    Monitor    Other peripherals
   |          |         |               |
   |----------|----|----|---------------|
                   |
                   |
                   |
         D6000 docking station (requires USB-C for functionnal triple display)
                   |
                   |   <=== Currently USB-A from the switch, I would like it to be USB-C (without having to use an adapter)
                   |
          |---- Switch ----|
          |                |
          |                |
       Laptop           Desktop