> Nobody actually says "I agree that you are feeling that emotion but I neither endorse it nor disagree with it" (in less formal wording). If you're going along with someone else's emotions, you're implicitly endorsing their reaction as justified.
Yes, actually, lots of people have healthy partnerships where they disagree with how their partner got into the situation, but can still recognize that the partner's feelings about that situation is valid, regardless, since it's an emotion their feeling, it doesn't have to be rational or logical and it's certainly not up to you to decide if it is/was neither.
This is what emotional support is, not validating their actions, but validating the emotions they're feeling, regardless of why. And not seeing some emotions as more "correct and valid" than others, they're all valid and correct, since we're humans after all.
> They share the emotion because they want other people to agree that the emotion is right and justified.
This, in your words "falls apart in the real world", because people don't speak with others always with the same intention, sometimes people want to vent, sometimes people want to manipulate, sometimes people are looking for help, and a whole other rooster of reasons. Most of the time, people speak with others about their feelings because they want connection.
I think you're stuck in trying to separate "valid, rational and logical emotions" from "the rest of emotions" while that distinction matters less than you think, and you'll be seen as very emotionally cold/distant if you aren't able to accept people's emotion because they aren't "rational" (or whatever reason you use).