The first what if you suggested is the one that will most likely bite you in the ass. If two candidates are similar and overwhelmingly popular, the more people that vote only for their most preferred are each making it more likely that the one candidate(s) they don’t approve of have a more competitive number of votes. It’s simply a bad strategy. While I think plenty will think that way in the shirt term, I would argue that the incentive is actually to not push that strategy, which will better serve everyone in the long term.
As for the lesser of two evils vote, that’s not a problem, that’s a feature. You can still vote for the lesser of two evils for the candidates you think has a chance AND for the candidates you actually approve of. The point of approval voting is to find the candidate that is MOST approved of. Even if angry single person voted for all of the candidates except their idea of the worst one, at the very least, that still eliminates the possibility of the least popular candidate from being elected. There can definitely be some spoilage there, an extremist candidate makes an easy target to rally against and a slightly less extreme though still fringe candidate gets more votes as a result, but it is still an unlikely outcome for them to have enough support to win a race that they are unpopular in.