Mutations occur in every species on a constant basis. Some make no real difference, some make it harder for the organism to survive, so those mutations simply die. The ones that give it an advantage survive and multiply. It is possible that the omicron mutation has only occurred in Sothern Africa, and because it is an improvement (from its viewpoint) it has prospered. It is also possible that is has occurred in other places but failed to survive for some reason. As you suggest, it may be that the background levels of HIV have allowed it to prosper, but in that case it would presumably fail to prosper in communities with lower levels of HIV. Time will tell! My suspicion is that it is likely just a better version that has got a foothold and then spread due to the movement of people, much as delta did....
It is worth remembering that even in a global pandemic there are people who are happy to use one situation to push a completely different cause. Just as the politicians are using covid as an excuse to knock their opponents, there are people (and groups) who would use it to push their own agenda. Whilst is is indeed possible that HIV has an impact on the spread of covid, it is also possible that covid it is a useful lever to forward the cause of those looking for funding for HIV treatment in Africa.