I don't know if it's a bug or intentional, but rapid fire weapons are really bad for stagger in AC6 because for some reason their low Cumulative Stagger rating causes the stagger to fall off faster in addition to causing less persistent stagger to begin with. So if you keep sustained fire up, the stagger from your older bullets will fall off in between shots, causing the target to not actually gain more stagger. I have experienced more than a few moments where my target began regenerating stagger while I was shooting them with the minigun because the stagger of the bullets that hit them 3 seconds ago has already worn off, despite taking constant fire.
Conversely, weapons with high Cumulative Stagger rating both cause more stagger per hit AND the stagger lasts longer, so single shot or low capacity weapons aren't even hindered by having to reload or overheating because the stagger they inflict reliably sticks throughout their downtime.
It creates this weird situation where the game just. Kind of lies to you by saying that rapid fire/automatic weapons are good for applying stagger and preventing enemies from recovering when that is just not what happens. I expect you can somewhat compensate for this by using dual trigger builds with two automatic weapons to double that stagger build before the Cumulative falloff, but it's still a bizarre issue that makes full auto weapons just markedly worse than single shot and burst weapons. Once I switched from the minigun to the Zimmerman shotgun, fights that gave me trouble were a cakewalk, and enemies consistently staggered, whereas the minigun had me tearing my hair out as enemies hovered at like 90% stagger while I unloaded on them.
If you're having trouble with full auto weapons, just try out a grenade launcher or shotgun and see if things get better.