You don’t get to take the “no effect” over the “small effect” just because you’re an atheist. That is precisely what taking faith over data looks like!

My answers would be that we're arguing over statistical noise.

I take what I consider to be the simplest explanation in the absence of a credible alternative, that prayer does nothing when the recipient is unaware of it.

I take that view because I've never heard an alternative explaination that didn't appear to break the second law of thermodynamics.

extraordinary claims require extraordinary evidence.

A magical, invisible, omnipresent, omnipotent "all known laws of nature defying"-being that answers prayers, requires significantly more evidence than a small effect in some meta study.

Absolutely. My point is that "I'm an atheist so I'll take the option that agrees with my personal beliefs" isn't a valid line of reasoning. You could symmetrically argue "I'm a catholic so I'll take the option that suggests there is an effect, albeit a small one". Now we're just arguing whose personal beliefs are right.

A more properly scientific line of reasoning would be to instead say that you'll assume the small-to-nonexistent effect is nonexistent until somebody produces a model capable of predicting the proposed small effect, or a myriad other arguments along the same general lines.