I got a USB C HDMI dongle that works with the Nintendo switch and out of curiosity I plugged in my note 8. It booted into Dex. I didn't realize you couldn't just use it anytime.

It was this MYRIANN 1080P HDMI Type-C Adapter Dock for Nintendo Switch, TV HDMI Converter Cable for Nintendo Switch (Silver)

But it needs more power than a regular USB brick so I got This UGREEN USB C Charger 30W PD USB Type C Wall Charger Adapter for Macbook, Nexus 6P, Nexus 5X, Nintendo Switch, Samsung Galaxy S8, Lumia 950 XL, Google

And this Anker PowerLine+ C to C 2.0 cable (6ft), High Durability, for USB Type-C Devices Including Galaxy S8, S8+, Google Pixel, Nexus 6P, Huawei Matebook

These work with the switch and my phone went into Dex mode when I plugged it in with these.