I definitely consider cannabis to have psychedelic-like qualities, though I would never consider it interchangeable with a serotonergic hallucinogen. These are definitely very different types of drugs on the whole.
As for the personal insights and self-examination, cannabis definitely does this for me. I actually considered it to be better than typical psychedelics for this when my tolerance wasn't so huge, my first few years smoking were actually some of the most personally transformative of my life, my mind was opening up in all kinds of ways it hadn't before. Psychedelics do this for me as well, but they simply could not compare to cannabis in how I was able to incorporate it into every single aspect of my daily life while it did this, it gave me all kinds of perspective that I just don't get from a typical trip, which seems more like a vacation from daily life to me. However, psychedelics are definitely much less limited in this way as far as pushing the dose is concerned, and I also find them to be much more emotionally fulfilling, and this allows for greater insights related to things like empathy. Also, now that I do have such high cannabis tolerance, the psychedelics are able to produce this kind of headspace for me with much more consistency these days.
With regards to the hallucinations, I do find there to be some overlaps as well, but overall I find the significant hallucinogenic experiences I've had with cannabis, mostly brought out through meditation, to be more similar to salvia, and what I've heard about from iboga. Things like floating through dark fantasy worlds or reliving memories from someone else's perspective as a path to emotional release were not uncommon, as opposed to how psychedelics for me are generally more abstract and tend to relate more to seeing some of the background workings of my mind. Both very useful, but very different. Unfortunately, these kinds of experiences on cannabis for me have also largely disappeared with tolerance.
So yeah, I can definitely understand the relationship, but I certainly don't think they should be treated as exactly the same kind of thing.
I really need to go on a tolerance break....