So far I have all the boxes full of wild pokemon in my emerald cartridge played on console, and only 2 wild pokemon are method 1 (shiny spheal and a skitty), all the others are method 2 and like 10 of them are method 4.
This seems to be a result comparable to the vba v24 that I used to rng as emulator, since I only rng and don't randomly capture, so the fact I haven't found any method 1 isn't far from the console reality, as the method 2 and 4 encounters seem to be comparable to console ones.
Also background music influenced pokemon box kyogre/groudon rngs, because I always had the same result without a background music triggering the dialogue with the legend, while I had different results with the background music because, even using the same states, triggering the dialogue at a different frame but still starting the fight at the same seed to rng the same spread, caused to or not to trigger the method 4. Also, only with the background music, some spreads are sometimes entirely skipped and the difference where you must trigger the encounter varied randomly a lot. Like, sometimes, a singular frame advance made multiple seed advancements.
This way, with the background music, you don't have to manually refresh the screen with the pokedex to make it possible to change the method.