I haven't tried any of the "real" psychedelics, but I can tell you my experience of insights I gained from high doses of pot, with almost no tolerance as there are many months to years between occasions.

It made me pay attention to different things than I would normally pay attention to - things I arguably should have paid more attention to. Specifically social cues. I would repeat peoples words in my head over and over. I would go over written words and try to imagine the tone of voice very carefully.

It also made me change my behavior (temporarily), partly as a result of the different way I was paying attention. I got to see how people responded to that changed behavior (they responded very positively).