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

I loved and would now if i could jump into a pile of leaves! Its fun and free-ing and wonderful. People do not harm creatures doing this If we send that pile of leaves off to live permanently under our trees or compost piles so that the CREATURES who will live in and off of those leaves will HAVE A HOME!

I am a conservationist first but i am also a hopeful ProBusiness human who wants their family friends gardening store businesses to thrive. I think what the business community could value from conservationist is NOT NO NO NO... but WHAT HOW and maybe for some even WHY!
I want to be able to go to my gardening store and buy the RIGHT TOOL to MOVE LEAVES, The most ORGANIC WAY to support a flower garden and GRASSY WALK WAYS since i do want to walk around my yard. I have no idea what this NEW GREEN GARDENING BUSINESS would look like but I want to spend my gardening money PROTECTING WILDLIFE NOT destroying it.
This requires first of all KNOWLEDGE about WHAT WILDLIFE NEEDS to live on our yard.
For me as a scientist trained person this means I CAN CONDUCT BASIC SCIENCE to help this along by documenting what is IN MY YARD and how i MAKE MY YARD MORE BIODIVERSE. I have done that since 2013 at least. Here are my pictures of what i have found.

LEAVES if they are freshly fallen I am not finding LOTS OF INVERTEBRATES on that. I find old wasp galls. I wonder when lepidopterans caccoon in my leaves? I am guessing it is an established LITTER LEAF PILE!??? What does that look like? How do we make a LEAF PILE FOR LUNA MOTHS!? and how can we COMPLEMENT THIS NEED with people honestly Needing to RAKE THEIR YARDS! we cannot just let things lay about. So one of the things i am paying close attention to when i photograph LEAVES is what condition they are in, where they are laying, maybe how long SINCE THE LAST LEAF DAY they have been laying there. Maybe count days from ALL LEAVES DOWN DAY!? it looks this year we are close to that day. We had a huge WOOMPF of leaves come day over the last week.