“and complies with USB-C™ 3.1 (Gen 1) specifications.” Therefore you and @janvlug should, please, follow kind advice from @ChriChri (use HDMI cable and HDMI ports on your N360/DA-70882 combo):
As pictured: https://forums.puri.sm/uploads/default/original/2X/0/007cd4e58c4aebf312c9e1293734a71efd46053f.jpeg
P.S. In addition, recommended power supply would hit 100% if used one from this category: https://www.shop-fsp.de/FSP065-A1BR3-with-connector-type-USB-C-5/9/15/20-VDC-65-W, but original Librem 5 power supply should negotiate PD toward DA-70882 docking station that I’m not familiar with, yet my advice is intended to be in general anyway, direction on how to connect things/achieve …, and in respect toward above useful, kindly shared solution.