This problem has been frustrating us for months now. In addition we thought the mods would not be loading because an "Earplugs" plugin was the culprit causing nearly all other mods to stop working.
Sometimes 1-2 mods show up when I check the server in the Arma 3 server list. When I check on the launcher it doesn't show any mod at all. We have about 38 mods. (CBA, Ace, Ares, RHS, BWMod, CUP, TFAR are the majority)
The weird thing is that we use Microsoft Azure, too. What are the odds that anyone even uses that here? We have used Hetzner before and the mods were always shown in the launcher for everyone to download comfortably.
We keep the mods in the workshop folders and directly load these instead of moving the folders to the main game directory as that is silly, but that is the way it was working for us for a long time...