i'm trying to figure that out myself. Some days I'm pretty good others I couldn't tell the difference between a chord and a note! To me it seems some dim and aug. chords have more than one sound. with one it's discernable with the other it isn't as easy.

I try to sing the last note and then decrease or increase it by a half step. Then, I sing the whole chord and figure out which version sounds right (decreased or increased by a half step). The 'sounds right' version is your neutral tone. So if you found your neutral chord by decreasing the last note, then what you heard was an augmented chord. If you found your neutral chord by increasing the last note, then what you heard was a diminished chord. Does that make sense? (it does in my head at least 😅)

You can listen for the fifths (dim or aug), but I listen for the resolution as you alluded to. If you have a piano or instrument around, play the chord and it's resolution again and again until you internalize it. For me dim wants to resolve up to min and aug down to major.

Try to perceive the chord as a whole. Feel its mood. A diminished chord has a denser structure—it sounds tense, while an augmented chord sounds empty. The difference in sensation is like a fifth and, for example, a sixth (one interval has color, the other doesn't). These sensations simply need to be memorized, and if you haven't encountered these chords before, it will take time. I, too, am stuck at a certain level and am trying to figure out what's going on))

Not sure a noob like me is in a good position to give advice, but I'm trying to get the interval between the highest and lowest note on the chord. Smaller interval - diminished, bigger interval - augmented

You sing a note you hear and then you sing a note a major third and/or a minor third above or below, at which point it should be easy to figure out which one sounds...if it sounds a minor third it's a diminished chord, if it sounds a major third it's augmented.

I've read and always thought of these words to describe them:

Aug – mysterious, dreamy, intriguing, thoughtful, curious
Dim – tense, uncomfortable, intense, anxious

Try making your own mind map/model of what they evoque. I know you said they sound dissonant, but it's not the same type of dissonance, you gotta get to know them better, as if they were your own friends. Takes a little time to establish a relationship. Look for examples in songs you know.