I've had that same experience, so the way I discuss detail is more in terms of mental effort. Highly detailed headphones allow me to perceive small details and textures in the music with less mental effort needed than with less detailed headphones. If the headphone is less detailed, then I have to know that a detail is there and focus on it to perceive it. If a headphone is more detailed, then that sound jumps out at me even when I'm not focused on the music. Hence, different headphones can be more detailed in some areas than others, and a "less detailed" headphone can in some frequency regions be perceived as more detailed than a "more detailed" headphone by having an FR that emphasizes the details in that region.

Another term that I've seen in place of detail that I find really helpful is "tonal contrast". I first saw the term used by reviewer Marcus at Headfonics, but the term probably goes further back than that. Tonal contrast is the contrast (think visual contrast) between different tones, like between fundamental and the overtones. Higher tonal contrast makes the differences between similar pitches on different instruments be more pronounced, which sounds like more detail. Human vision, object recognition in particular, is more dependent on contrast and silhouette than color. That's how optical camouflage works, not by making an object impossible to see with the eye, but harder for the brain to recognize as a given object. To me, detail is music is similar. You're always hearing that sound that comprises a detail, but your brain didn't recognize it as an instrument or whatever, until you heard it on a headphone with higher tonal contrast in the relevant frequency bands.

All of this should just be encapsulated in the FR (plus psychoacoustics), but it's a very fine-grained and multi-band look at FR that we currently don't know how to do accurately or reliably. It's not just more treble, as I've heard very treble-heavy headphones that masked detail due to having too much treble. And it's not just having an even or neutral frequency response either, as an unbalanced FR can highlight certain parts of sound, which can make them sound more detailed than a headphone with a balanced FR. Then there's also distortion; sometimes distortion can improve clarity by boosting relevant overtones and thus increasing tonal contrast. So yeah, it's not something that's easy to recognize from just a graph.