Ok, so this is tricky.
So, generally this would be the kind of situation where plausible deniability is important. Actually knowing what Ling Qi and Fu Xiang got up to would be exactly the kind of thing that most leaders would desperately not want to know, because it creates massive problems for them. They'd rather quietly stay in ignorance.
The problem here is two-fold. Firstly: is Cai that sort of person? Second: we have already arguably gotten her involved. By framing someone like that, if Cai lets things go ahead an injustice will be committed under her authority. This, as others have noted, tramples all over her ideals and the rule of law. This isn't something she could just stay ignorant of and let everyone move on past - it directly undermines everything she's trying to do.
But what about trust? This is a difficult thing. Firstly, I would not frame "trust" as trusting her to let us get away with this. That would be blatant corruption, and strongly against everything we've seen from her. And, frankly, for all the people who say "if she does anything then we know we can't work with her", I'd say that that's ridiculous. We are the ones who created the problem here. We didn't have to do Fu Xiang's favor like this. We could have said that undermining her order and justice like that was unacceptable, and offered to do something else. We didn't. Working with her just entails taking responsibility for our actions, accepting whatever punishment comes our way, and
never doing shit like this again. That's hardly a dealbreaker. Hell, having a boss who actually pushes us to be a better person is arguably something Ling Qi would like - it's better than our other role-models (Meizhen and Xiulan).
To those who say "she wants us to be a spy, things like this are expected" I disagree. There are a lot of things we can do that aren't trampling all over her justice. Gathering intel, acquiring politically awkward blackmail, acquiring evidence of crimes so justice can be delivered, scouting, sabotaging enemies in war... This are all things our sneaky skillset is helpful for. They are not anti-justice in the same way that breaking the law and framing people so that they are unjustly punished is.
THAT BEING SAID. Do I think that confessing is the right idea? That's more tricky. Confessing makes life very difficult for everyone. It would likely have serious long term consequences for our relationship with Fu Xiang that could cause us a lot of trouble. Long term, minor crimes done in the Outer Sect aren't anything anyone will really care about later. They're only an issue right now. Confessing doesn't help anyone it is important to note. It is purely a manifestation of Ling Qi feeling guilty, and not wanting to lie to Cai at all. Telling the truth, however, doesn't help Cai, doesn't help Ling Qi, and doesn't help Fu Xiang. It's bad for everyone. Of course, one could readily label that an excuse to take the easy route out, and this would not be invalid.
Confessing gives us Ling Qi taking responsibility for her actions, and paying penance in order to cleanse her conscience. Then, perhaps, we can move on and strive to be better in the future (though with a lot of people pissed at us, and a lot of political trouble for Team Cai, and ... yeah).
This might just be taking the easy route out, but I would prefer Ling Qi to a) stay silent, and b) reciprocate by sharing why she wants to be a better person, and what she's done in the past that she doesn't want to do again.
And to feel really guilty about this whole mess and endeavor to be a much better person in the future.
We have hinted at our ideals in our past conversations with her - our dislike of the behaviour of cultivators in the outer sect, and our support for her goals - but we haven't really opened up about why we support her to her. We've only really obliquely discussed our feelings about our past in that recent conversation with Meizhen. I would argue that this is the ideal time to open up about to Cai about why we want to be a better person, and why we've supported her against the arguments of Sun Liling and Chu Song. If this whole scene is about us establishing mutual trust and a more personal connection, then sharing our feelings here is, I would argue, what we should be doing.
@yrsillar if we don't confess here, will it result in the conversation just ending without us reciprocating to Cai at all? Because that doesn't really feel right.