After Chrome and Firefox, I tried Puffin, iexplore and Opera, same result.
Then I tried to create a new account, and managed to finish the tutorial and first mission.
So it HAS to be from their side.
(and I sent a new ticket, but nothing came back yet)
ps: I just had this crazy idea on the discord channel: by any chance, did you get any new unit recently?
Tuesday evening, before my last disconnect, the priority gacha gave me 3 new units, and the problem appeared between then and 3hours after, so I'm wondering if it's not related to one of their assets