Been noticing this for a couple of years now and couldn't work out if it was confirmation bias or something genuinely repeatable. I do most of my recording in old buildings around Yorkshire and the full moon sessions consistently produce more static and what I'd call "layered" interference - like multiple signals overlapping rather than clean white noise.
My working theory, and I'm not sold on it entirely, is that the ionosphere behaves differently during high geomagnetic activity which full moons can sometimes correlate with. That could affect radio frequency bleed into cheaper recording equipment. Nothing supernatural necessarily, just physics doing something odd.
That said, I've had three recordings from full moon nights where the interference itself seemed structured rather than random. Hard to explain without sounding daft.
Would be interested to know what kit other people are using when they notice this. I'm on a Zoom H5 which picks up a fairly wide frequency range and that might be part of the problem or part of why I'm catching it at all.