The WD15 arrived. With already up-to-date firmware installed within, so I didn't need to fuss with a Win10-from-USB setup to update that. All other system firmware is Linux or BIOS update-able. The included (130W here) power brick is just a standard Dell laptop brick with the big fat "white" DC tip.

It works. Just plugged it in, and it worked. Plugged in monitors, and they worked. Selected HDMI audio output in Pulse, and my videos play sound through the speakers of the first monitor (HDMI).

Power button on the dock works to wake the system (and probably also to power it on from completely off).

One minor complaint: No "on/off" LED on the dock, so it is not obvious if the system is starting up or not after pressing that button. Instead I wait a few seconds for the monitors to come out of standby before I know it's alive.

Unplugged the USB-C cable while watching a video, and the desktop/video reverted to the 9360's built-in screen, and it all continued to play.

So.. passes all tests thus far without me having to do anything special.

EDIT: Another quirk just noticed: when plugging the USB-C dock cable into the 9360, the notebook always wakes up. Despite the BIOS setting for "wake on AC power connect" being turned off.