If it's not Sauromon then obviously my criticism is wrong and is based in my simply watching the Peter Jackson movies too many times. But, if it is Sauromon then I would not buy that Gandalf would fall for the sudden change of heart to the point that he fully trusts him and can't imagine that he would betray him.
And, at this point, once you confirmed The Stranger is Galdalf it's time to stop with the we are hiding who this character is stuff. I mean if I'm being totally honest, we all knew it was Gandalf by the middle of season 1 if not before so the whole thing became kind of pointless. Continuing that with another character would be a bad choice IMO. But, that is a quibble in an otherwise enjoyable show.
It's not up to the original Peter Jackson movies but no TV show has the time or budget to do that level of work and I still think they did a good job given that it is TV on a streaming system that most people get as a bonus when they were already going to have Prime.