My experience with Nextcloud  using webDAV to share files with kodi has been rather dissapointing so far.
I had no problem with my home router when accessing the WAN ip from inside the LAN. There would be double traffic on the LAN with the routing detour but should be no much of an issue for this aplication (all this traffic would never leave the LAN).
jakob the path to access my nextcloud server includes the 'nextcloud' parent. Not sure if removing it as you did could be causing you trouble.
But it takes ages to start playing any video even as small as the default 4MB Nextcloud intro.mp4 one.
Anyway the issue doesn't seems related exclusively to kodi because from my desktop using nemo there is no much difference, to the point of being useless.
You can happily browse all the directories and files but as soon as I try to play any movie it gets stuck there.
So as Borygo77 I also use a VPN to access my kodi library (OpenVPN running on my main server).
 linuxserver.io's nextcloud docker stack running on my main server, kodi runing on a RPi3B