It doesn't seem like there's a limit to how big they can get just a limit to how quickly they can get bigger due to what's called the Eddington Limit which explains how matter falling into the black hole emits radiation and if enough radiation around the accretion disk builds up, it can overcome the pull of the black hole and push matter away, at least until enough matter is pushed away that the radiation levels fall back under the limit and matter starts falling in again.

PBS Spacetime had an episode somewhat recently about a black hole which is growing at many (hundreds? thousands? I forget) times the Eddington Limit. And, as far as I remember, it isn't the only one to exceed the Eddington Limit - just the one with the record for how much it exceeded it.

I'll try to dig it up when I'm not at work (or if I remember the exact episode through the day).

Importantly, the Eddington limit does not apply to black hole mergers, theoretically allowing as much growth rate as you're able to feed in from smaller black holes.

So then the only theoretical limit on black hole mass would just be how fast you can put matter in black holes and/or merge existing black holes versus how fast the universe expands?