Very very odd : I made a second network on the Ubiquiti access point. The first one was 2.4Ghz and 5Ghz, this one I made as 2.4Ghz only. Same password (I copied-pasted that password in my previous attempts, so I was 100% sure it was the same, no extra spaces either in the copy-paste).
With the 2.4Ghz only network it connects like a charm. Go figure...