The only benefit of having a zoned receiver if sometimes you want the same source to all zones. If you don't plan on doing that, I would get 3 receivers if you want separate sources.

Could I control them through the Heos app?

And, if I did want the same source to all zones, could I still do that with 3 receivers?

I don't really know much about HEOS, except that it's brand-specific. If you have three receivers and they are all HEOS compatible, then perhaps it would work, but if you want the same source going through three separate receivers, then you would probably have to run wires to each of them. I would guess in your situation, you should get a receiver with three zones, if they exist.

I'm assuming you have a Denon since you mention HEOS. My Denon (3-4 years old now) handles 3 zones independently especially since you're already wired for it ... Easier than 3 receivers IMHO.

https://support.denon.com/app/answers/detail/a_id/74/~/multi-zone-application