One criticism people like to level against Approval Voting is that people will “tactically vote” with a “bullet” vote where they limit their support to a single candidate despite other candidates being appprovable to them. I would classify this as a “sincere” tactic since if that ballot was the single ballot deciding the election the person who cast it would be happy.
There are some tactics which are insincere such as “Favorite Betrayal” where you don’t actually want your ballot to be the single deciding ballot but you filled it out to try and game the system against other votes and you want to influence the order of eliminated candidates to try and help your ultimate favorite. This kind of tactic would be insincere.
So while Approval Voting is not Strategy proof for people with trichotic preferences none of the tactics used in Approval Voting are insincere which I think puts it above systems like Rank Choice Voting.