XPS with WD15 Dock does not work with KVM

@Boris C  there are a few issues here.  First as a general note, when asking about technical issues like this, it helps to provide technical information.  In this case, identifying the exact system model you have -- like XPS 15 9570 or whatever -- rather than just "new XPS" would be useful.  Second, since you're dealing with a KVM it would help to identify the specific model rather than just the brand and connector types, and third it would help to identify exactly what cables/connectors you're using between the dock and KVM, since there are some potential pitfalls there.  For example, if you're trying to connect one of your displays from the WD15's HDMI output to an input on the KVM using an HDMI to DisplayPort cable, that will never work because HDMI to DisplayPort cables only allow you to run a DisplayPort source into an HDMI input, not the other way around.  A DisplayPort input can only accept a DisplayPort signal, and the WD15 only has a single (mini-)DisplayPort output.  And even if you connected a DisplayPort MST hub to that output in order to split it into separate outputs that could each be used independently (thanks to the magic of DisplayPort MST), you'd still be facing the next problem I'm about to describe.

The second issue is that trying to run dual U3014 displays from a WD15 is a problem all on its own, as you already found by the fact that you can't get full resolution on both displays.  That's because as noted on the WD15's product page, FAQ page, and manual (available on support.dell.com), the WD15 can only handle dual displays up to 1920x1200, or a single display up to 2560x1600.  That's related to video bandwidth limitations on regular USB-C connections.  But since you have an XPS system (again, specific model would have been useful), your system very likely supports Thunderbolt 3, in which case you'd be able to use a dock like the TB16 (essentially the Thunderbolt version of the WD15) or its replacement the newer WD19TB.  Either of those would be able to run dual displays up to 4K 60 Hz.  And since the WD19TB in particular has two full-size DisplayPort outputs, that would simplify setting up your KVM.  The TB16 also has dual DisplayPort outputs (one mini and one full-size), which would work with the correct cables, but the TB16 doesn't have a great reliability track record, so I'd recommend the WD19TB.

Lastly, have you even confirmed that your StarTech Dual DisplayPort KVM of an unspecified model type actually supports dual 2560x1600 displays?  Not all KVMs with dual DisplayPort outputs support that much resolution per display.  But if yours does, then I suspect you'll find that if you replace the WD15 with a WD19TB, you'll get both displays running at maximum resolution and through the KVM.