I have no data and just one fall of casual observations but so far my working hypothesis is that dry leaves recently fallen have the least living organisms associated with them. IF this holds true then raking early and often would be the best way to schedule your yard raking. You are moving the leaves just as they have fallen and before they gather a lot of moisture. It seems to me that wet leaves attract collebolans pretty quickly. Certainly as leaves decay they will be releasing nutrients and attracting life. As they grow fungi they will attract tiny animals.
As an example of what i find with leaves fallen, rained on and not raked for more than on e week or so I start to see mushrooms growing that were not on the bare multispecies lawn of grass, wildflowers and moss I am observing. 12-13nov2022 I posted the same individual tiny mushroom I marked and rephotographed a Bonnet Mushroom possibly. This delicate Bonnet Mushroom was growing from my leaf litter on my front lawn yard! The cap is tiny about 1 cm tall and the ghostly white smooth stem is snaking out from under the wet leaf litter for several cm. If i rake this the mushroom perishes... We Human GIANTS need to pay attention to the smaller lives we may disrupt and think about if we need to do that... My lesson is too rake early and often when the leaves have just fallen and when they are dry. As soon as the wetness takes hold LIFE EMERGES!!! so it is timing for when to rake... maybe less ↑