We don't know if there is "natural" immunity to HIV. There have been at least a dozen* reports about people that should've had HIV, but never developed it. Read "should have" in a statistical sense.
Research in that field is still ongoing, but at a very slow pace. Just like they are still looking for people with natural immunity to COVID. In both cases, it's like looking for the needle in the haystack, as people with natural immunity are very rare. In the case of AIDS, the research is being done in exploited communities (read: forced prostitution), which makes it even harder.
In the case of AIDS, you can't "experiment" at all, since AIDS renders the entire immunity system inoperable. COVID just attacks your lungs, in general. And, again, AIDS can be easily avoided. You can't avoid COVID in the long run.
Only newborns have no or very little natural immunity**. The rest of us have a lot of natural immunity for an incredible number of diseases in our immune system. That's why a disease that takes down the immune system is very serious, as you could die from a simple cold.
It's also not a simple black and white thing. People with sickle cell disease, for instance, have natural immunity for Malaria. The reason is that having sickle cells amongst your red blood cells gives our immune system the time to respond to Malaria. In healthy people, the Malaria parasite reproduces so fast, that by the time the immune system gets to work, it's too late. The parasite has reproduced and changed so much, the immune system doesn't know what to fight and starts attacking other cells. That's also the reason why Malaria causes chronic very high fever. Malaria can't attach to the sickle cells, so it develops at a much slower pace and changes much less, so our immune system effectively kills it after a while. There's still fever, but much less and only once.
And even when these people with natural immunity are found and scientists are able to find the DNA sequence that provides it, it isn't certain it's possible to introduce that DNA sequence to others. It might have other repercussions, fi.
*Take into account I've read about this years ago and my memory is less than perfect these days.
**Scientists suspect there is some form of natural immunity inherited in our DNA. AFAIK, that hasn't been researched widely, so it's just a theory.