Yeah, that's my interpretation too. Otto's pretty scheming, but I don't think it's necessary to assume that he was spying on Daemon or Rhaenyra in particular.

Mysaria seems to have established herself in the ifnormation business since returning to King's Landing, with kids who she pays to gather information for her. In general if you're in that business, it makes perfect sense to have some of your spies hang around brothels keeping an eye out for anyone important entering - Mysaria herself had first-hand experience with the potential value of information that can be obtained in a brothel after Daemon got disinherited due to the "heir for a day" incident (and I'm guessing that's not the first time she saw or heard something incriminating in her time their).

So yeah, Mysaria having spies hang around brothels keeping an eye out for anyone important entering makes sense. And if you're getting into the information business and looking for people to sell your info to, the hand of the king seems like a pretty good potential customer. So at some points in the past she's sold him valuable information, and it's always proven true, so she's become a trusted source. And is it really weird for the hand to not tell the king the exact details of every single informant he has? I could see that being the kind of thing where it's just seen as an unimportant detail - the hand's job is to get the information and advise the king, the king's job is to act on it.

So Mysaria having spies keep an eye on brothels isn't a sign of Otto doing anything sketchy. And her selling that information to Otto isn't necessarily sketchy. And Otto not telling the king about his sources isn't emcessarily sketchy.

Is Otto scheming and plotting? Oh, absolutely. He's been trying to get more power since before the show started and he's been scheming to get a grandson on the throne since the moment Aemma died, if not sooner. Was he probably thrilled when he got an incredibly incriminating report about Rhaenyra and Daemon from a trusted source? Yeah, definitely. But was he specifically sending a network of secret spies that he deliberately kept hidden from the king to follow Rhaenyra and Daemon around looking for something incriminating (and hitting the jackpot)? Not necessarily. That might have actually happened as part of the regular, non-schemeing part of his job.