The one-arm signal though is a palm out to indicate you have the ball you have an advantage. Plus where is the actual foul?
It’s not really clear to me if he formally was playing advantage or not. Referees will use one or two arms held out horizontally to indicate advantage. As you said there was no foul but neither of these things matter.
Firstly he could have thought there was a foul and was waving play to continue.
However he restarted the game with a drop ball which means that he had stopped play, presumably to give the keeper treatment or more likely because he thought the keeper had misinterpreted his decision. Since when can the referee stop play because he thought that the keeper had messed up?
If he was playing advantage then he would have stopped play and awarded the free kick.
For me, the referee then does some “quick thinking” and realises that everyone should play to the whistle and he cannot stop play just because one player is confused. He then remembers that the keeper had gone down and then the referee tells the keeper that he needs treatment even though it is clear that the keeper was in no distress.
I think the club should insist on audio and an explanation as there is no logical reason for what the referee did and in effect he robbed us of 3 points.