Also, He's familiar with Halbrand and has already seen his council to be wise and serving his interests. So, it will make that future corruption easier. And he still has his 'fair' visage.
I think Halbrand was a useful comparison for Galadriel. How she takes that darkness and converts it to want justice. Whereas he is seeking dominion.
Looking back on the reveal, which was pretty well tipped off, you really can see all of the clues pretty obviously. To me, it's always been about that fight for the smith's token.. he was just too brutal. But when Adar first saw him and had terror in his eyes.... you don't get scared like that over any human. I do wonder if that line about taking someone from him was just a lie to divert the truth, or a jab at something he did.
Now, in the books, Galadriel, Elrond, and Gil-Galad don't trust Annatar (and I think eventually Celebrimbor realizes it after he makes the rings), so they never fully fell for it and when Sauron eventually makes his own ring, they felt it and took theirs off immediately. So, in the show, that's mostly shown by Galadriel who starts to piece together that something is off.
Now, I do think one question is that if Halbrand is really Sauron, why did that blade injure him so badly, and how was he healed by Elvish Medicine. But perhaps Maia in human form just are that way?
I don't recall exactly where this is from, but in this One Wiki article on Eonwe, it discusses that Sauron originally asked Eonwe for forgiveness (real or maybe a ploy) and he was told to ask the Valar.
https://lotr.fandom.com/wiki/Eönwë
So, I think that's a reasonable explanation for why he's out on the sea. Maybe the big monster in the water was their response. Maybe he also saved Galadriel for two reasons.. 1, he did want to corrupt the elves, but 2, maybe in that moment he thought that was the best chance to not be destroyed by that monster.