U2722DE, multiple monitors, KVM, XPS 13 2-in-1 and desktop PC

@LivingInTheGreen  The good news is that your envisioned setup will work -- as long as your desktop PC supports audio over DisplayPort as well as DisplayPort MST for daisy chaining, but those have been around for a while, so the likelihood is high there.  To address some specific questions you asked:

• The KVM function cuts over the entire USB hub built into the display, so any USB peripherals connected to the display will switch between host systems, including a webcam -- not just keyboard and mouse peripherals.  You will however need a separate USB connection between the display and your desktop.  I just mention that because you didn't mention it in your described setup, but while the USB-C connection for the XPS will carry video, power, and USB data over a single cable, the DisplayPort cable you're using for the desktop won't carry USB data.  For the desktop, you'd use the USB-C to USB-A cable to connect the USB-C upstream data port (not the USB-C 90W input) to your desktop.
• I'm not actually sure how Ethernet would work in terms of KVM functionality, and the U2722DE User Guide doesn't address this.  Technically it could go either way, since the Ethernet interface is just a USB Ethernet chipset built into the display, which means it could potentially switch between being available over the USB-C laptop input as well as the USB-C data-only upstream port, just like the other USB peripherals that are switched via KVM.  But I could see a case for designing that Ethernet interface to only be available to the USB-C 90W interface and not over the other USB-C upstream data port, the idea being that typically you'd use the former for a laptop that might not have built-in Ethernet, while you'd more likely use the latter for a desktop PC connection that would be more likely to have Ethernet and wouldn't need that from the display.  You might get a response here from somebody who has tested this, but otherwise I'm not sure else to say given that the manual doesn't provide clarity on this item.
• In terms of your dream setup, you didn't specify which generation of XPS 13 you have, but the new XPS 13 9310 is the first model with the Intel Xe GPU, which supports up to four simultaneous displays.  And even the last several generations of XPS 13 before that one have a GPU that supports up to three, so yes you would be able to run both external displays and your built-in display simultaneously.

For additional flexibility, another option would be to run an additional video cable from your desktop directly to the second display.  Why?  Because that way you have the choice of having the displays in daisy chain mode either both running from your desktop, or both running from your XPS, OR you can manually switch only the SECOND display over to the input that's connected directly to your desktop, in which case you can have one display for each system.  But then you'd want a more elaborate KVM solution, such as one that allowed peripherals physically connected to one device to control another one over a network connection.  Synergy, Mouse Without Borders, and Logitech Flow all offer this.