The pH effect is quite small in the presence of CYA
Maybe a few graphs to make that a bit clearer.
Let's start with this one:

(Graph 1)
This is what everyone has in mind when saying that pH affects chlorine effectiveness. And this plot - with concentrations of HOCl and OCl⁻ plotted as percentages relative to the sum of the HOCl- and OCL⁻-concentrations (which in case of CYA=0 is just FC) - remains valid whenever you have chlorine dissolved in water.
Now we plot that (still no CYA involved) not as a percentage, but in concentrations:

(Graph 2)
Pretty much the same plot as before with ppm (or mg Cl₂ / L) instead of %. I have chosen FC=0.092 because it yields [HOCl] = 0.05ppm (I am using the notation [...] for concentrations which is usually used for mol/L, but it makes the writing a bit easier), which is a typical TFP target range [HOCl], at a pH of 7.4 (which is the centre of the "classical" range between 7.2 and 7.6).
Now I am adding 30ppm of CYA to the equation and bump up FC to an appropriate target level, which changes Graph 2 to:

(Graph 3)
Most of the FC is now attached to CYA, called "CYA-Cl" in the graph. Zooming in on the bottom two curves:

(Graph 4)
You can see that the pH-dependency of [HOCl] is now much flatter. At pH 8.0, [HOCl] is 0.05ppm - the same as with FC=0.092/CYA=0 at pH=7.4 (which was the reason why I have chosen the odd number of 0.092 for the example).
But when plotting [HOCl] and [OCl⁻] not as absolute concentrations or relative to FC, but relative to just the sum of [HOCl] and [OCl⁻], you get exactly the same picture as above (Graph 1) again:

(Graph 5)
The equilibrium between [HOCl] and [OCl⁻] hasn't changed, but it's not the only relevant equilibrium anymore.
To summarise, a final plot of [HOCl] for CYA=0/FC=0.092, CYA=30/FC=4 and CYA=80/FC=10.3 all in one graph. Both scenarios with CYA yield the same [HOCl] at pH=8.0 as CYA=0/FC=0.092 at pH=7.4:

(Graph 6)
You can see how much flatter the pH-dependency of [HOCl] is with CYA. It allows pH-maintenance between 7.6 and 8.0, while staying within a much narrower [HOCl] band compared to maintaining pH between 7.2 and 7.6 without CYA.
Even at pH=8.4 you are still well above the grey bottom limit (but I wouldn't recommend to target such high pH for metal staining and calcium scaling reasons, and you have relatively high concentrations of OCl⁻ - see Graph 4 - at this stage that is more susceptible to UV-decay than HOCl - one of the reasons why we advise to lower pH before a SLAM, not because of chlorine efficiency, but because of higher losses to UV).
You can see that CYA allows pool operation in a pH-area that is a lot less affected by pH-rise due to CO₂ outgassing.
You can also see how little HOCl you actually need to keep a pool sanitized and algae free, and that the barn gate "classical" range of FC between 1 and 10ppm regardless of CYA is absolute insanity. It allows under- and over-chlorination to disgusting degrees.
So when someone makes you a compliment that you have such a clean pool with obviously hardly any chlorine, then they are actually absolutely right: You have very little of the chlorine species that matters. The bulk is kept in storage.