so long as everyone votes honestly
That's a big ask. If I think the vote will probably end up between two candidates I would be fine with winning, I am incentivized to only list the one I prefer. Likewise, if I think the vote will end up going to one of two candidates I would generally not be fine with winning, I am incentivized to list the one I perceive as the lesser evil regardless of my true preferences.
In the end, approval voting comes down to ranked choice voting, but instead of giving ranks you pick a rank threshold where everything above that rank is approved and everything below disapproved. The choice of that threshold is very vulnerable to strategic voting.
I do agree with you that it's in most cases a better system than plurality though. Even if you strategically lower your threshold to put a lesser-evil type choice as your lowest accepted rank, you do still hand in an approval vote for every candidate above that one. Vice versa with disapproval and strategically raising the threshold.
I disagree.
Let's say there are 4 candidates, A B C and D, and a large group of people have them in that order of preference, their (honest) acceptance would be A and B, but they'd much prefer C over D if those were the only two options.
A prominent forecast comes out and predicts a tossup between C or D. They all act in self-interest and strategically list A B and C as approved, to lower the chance of D winning over C.
Now that forecast was wrong about A's low chances for whatever reason and had they solely and honestly put down A and B, A would've barely won. All of them adding C doomed them to have to put up with someone they don't honestly approve of.
As you said before though, if we take this scenario into a single vote fptp system, we have all of them giving their single vote to C. Not only does this harm the chances of A winning even more, it also reinforces never voting for A as "A doesn't have a chance anyway and voting for A would be a wasted vote".
You can also construct a similar scenario the other way around for leaving out a candidate the group would approve of.