I've updated all my drivers on my laptop to the latest versions and I'm all out of ideas right now. Should I use a displayport connection instead of HDMI? Or is there something not right with my laptop setup?
Just wanted to report back with the solution that worked for me. The single (4k 60hz rated) usb-c to hdmi adapter (with HDMI 2.0 cable) unfortunately did not work for me. Even though it was single purpose as suggested by one of the replies.
If you run into the same issue with the 9560 version of the XPS 15, get a usb-c to displayport 1.2 cable. That is the only thing I got working and believe me, I tested a lot of different products.
@RuudBijkerk With an XPS 15 9560, you're only going to get 4K 30 Hz from multi-purpose adapters like that. The reason is that the adapter is setting up the USB-C link to support carrying video and USB 3.x data simultaneously. Supporting USB 3.x requires two of the four high speed lanes in a USB-C connector, which means you only have two lanes rather than four for video. That cuts display bandwidth in half, and on a system that only supports DisplayPort 1.2/HBR2 over USB-C rather than DisplayPort 1.3/HBR3 over USB-C, half bandwidth isn't enough to run 4K 60 Hz, which is why you only have 4K 30 Hz.
The only way to run 4K 60 Hz from that system over USB-C is to use a setup that would allocate all four high speed lanes to video, as a USB-C to HDMI 2.0 cable/adapter plugged directly into your system would do. But then of course you lose the multi-purpose adapter capabilities. Technically you could run USB 2.0 data simultaneously if you found an adapter that would do that, which is possible because that runs over separate pins in a USB-C connector dedicated to that purpose -- but I haven't seen an adapter like that. The only other way to run 4K 60 Hz with USB 3.x from that system is to use an adapter or dock that taps into Thunderbolt, in which case you can actually run dual 4K 60 Hz and USB 3.x simultaneously.
Newer systems that support DisplayPort 1.4/HBR3 over USB-C can run 4K 60 Hz and USB 3.x simultaneously even over regular USB-C if the device on the other end supports it, but again you don't have that.