Again, this is an information issue. Snape is aware that Su Li is interested in pursuing Harry, but he believes it is the normal sort of pursuit --- strong husband, familial alliance, wealth, etc. --- he has no idea that she is pursuing him in bad faith. He's looking forward to the girl pursuing Harry aggressively only for the tables to turn when she learns of his nature.
I think it is kind of sad that I think it is more likely that the adults noticed and just don't tell, so he learns rather hard lesson when it comes to trusting people rather than them not noticing.
The problem here is that Su Li is acting openly, in rather obvious ways that show that she has knows at least some of what she is doing to anyone with some experience and Harry is quite important, is a kid, is head of his house, and doesn't have family to point certain things out to him.
Someone approaching him like she does (ignoring all her internal dialog) should raise all kinds of red flags for people that know just how fucked up the world is, knows about how fucked up politics can get, so it just screams bad faith and is at the very least worth to point out and give a warning for.
The kids and Abigail are unlikely to notice the because they just flat out lack the experience, but I fully expect the staff to notice that how she is acting and the topics that were/are raised should get them to at the very least warn him about Su Li doing this in bad faith. Her not being local makes this worse not better as sad as that is as it is hard to know how is pulling her strings, goals are unknown, etc.
Apart from that Su Li is not even half as good at actually manipulating people as she thinks she is (at least from what was shown), she doesn't actually have direct adult supervision with already gathered information to point her at a target, help smooth things out and help plan things out, she also had to gather seemingly most information herself.
Basically she seems to be lacking all the support infrastructure someone would get if they were actually an important/valuable asset.
That all point more towards her being an asset that they can stand to lose without gaining anything and maybe get some information about the local politics.
Edit:
There is also the interesting part where she finds out he is a dragon, because it could mean that she just flat out flips or at the very least tries to talk with him and hope he is reasonable before he finds out that she was working in bad faith and bad things start to happen.