Well I think "it depends" is a good start to the answer.
Given: 2 different manufacturers will yield (on many occasions) 2 different points of impact at varying distances.
Given: 2 different bullet weights will yield different points of impact at varying distances.
Desired result: POI the same for all brands and weights at varying distances - not likely unless the distance is pretty darn close and the acceptable group is larger than a singular ragged hole.
I try very hard to only carry ammunition that is by a singular manufacturer. I (am old school) carry alternating HP/FMJ in my magazine(s) in the same weight, from the same manufacturer for EDC. I check my POI for both HP and FMJ and for what I shoot it seems to be same out to about 25M. I notice a slight difference (due to aerodynamics I assume) at longer differences - but less differences than when I compare bullet weight differences.
I still have some 115gr 9mm, that I use for larger steels in 3 gun - cheap hits close to 124gr, easy peasy. But I am more concerned with POI on my EDC, which is where I suspect it is more relevant, and have only purchased 124gr (of any manufacturer) for a the last few years. My AR9 seems to like the 124gr better than the 115gr as well, I notice a slightly larger grouping with the 115gr. I really do not notice any recoil difference.
I also limit myself to a small group of manufacturers, because a few that my friends have used can be much dirtier and less consistent (Winchester White Box for example) than others (Federal, Hornady, - favorite is Black Hills across the board). Each shooter will have their preferences, and the amount of deviation in POI that is acceptable is an individual thing. If I could get it to zero, without having to reload(!) I would take it! I just simply do not have the time to reload (used to and then life happened!🤣🤣) Now I have to choose between reloading, building new guns, shooting, practicing and the rest of life - reloading is the easiest one to give up!