I did not RTFM before starting to use DAVDroid on my LineageOS-powered Huawei Honor 5X. As a result, my contact categories were not transformed as groups, as explained here. Now I've chosen the right option and If I change a contact's category, it appears on my phone as a group.
But to sync my previously defined groups, I had to assign all my contacts to a dummy category, sync, delete that category and resync. An option to achieve the same result automatically would be great!
Thanks for the wonderful app.