“I’m fine” is a lock. “I’m actually kind of overwhelmed” is a key.

The standard answer is not exactly a lie. It is a door that closes politely, and once it closes the other person has nowhere to go, even when they asked because they genuinely wanted to know. Most people will not push past it, not out of indifference but out of respect, so your reply decides what happens next.

You owe nobody the longer answer. If you do want the conversation, one honest clause is usually enough to start it. Pick whoever is most likely to take it well and say the smaller true thing instead of the automatic one.