Native Spanish speaker here (ES-MX, specifically, if it matters). I think this is one of the cases where a solid general rule breaks down in the specifics.

You are correct about the difference between "ser" (to be, permanently/over an indeterminate time) and "estar" (to be in a particular state right now). But "No soy feliz" sounds perfectly idiomatic to me, even for a relatively transient state of sadness. ("No estoy feliz" doesn't sound wrong to me either, but feels just slightly less natural than "No soy feliz" even in a context like "No soy feliz ahorita", with an explicit "right now").

As a note: "No estoy contento" (Also "I am not happy", or maybe "I am not in a good mood") is definitely "estoy", rather than "soy". No clue why "No soy feliz" does feel idiomatic.

Thanks for taking the time to write this. As you probably guessed, I'm not a native Spanish speaker. (I should have mentioned that in my comment!)

You are correct, but I'd say this one is fundamentally ambiguous (I'm Portuguese myself, where this also applies), as it is a one-to-two mapping here. Without further context you can't really choose one or the other, so we just left it as is :).

I've always found it most painful trying to figuring out when to use verbs that translate to other verbs depending on context. It's just personal experience of course, so not sure if it really matters that much between all languages or types of learning.

Maybe a hint which one is intended in this case would be useful/possible or a hint that it could be ambiguous/other translation possible? I've built a couple of tiny tools for myself to learn languages and I've always run into the same issue with ambiguous translations. I usually ended up with adding some personal reminder or sometimes just (1)/(2) to resolve it, but I never found a consistent resolution for it.