As PPs have said this is an extremely difficult to treat mental health issue which is thought to relate to OCD and trauma so it's an awful position to be in.
Will she even let you sort and label things, OP?
If you bought a whole bunch of shoebox-to-drawer-sized, see through, lidded plastic boxes, would you be allowed to organise things into them - not throw any out! But e.g. one box "baby clothes, 0-6mo, not sentimental, stained", one box "DC name, outgrown clothes, sentimental", one box "DC name toys, outgrown, eBay value £0-5" and so on. To be honest that might take a couple of years of solid work.
Get shelving in. You still will have THE STUFF
but at least be able to see there are no mice/moths/mould, and be able to safely move things for access...
It would at least reduce trip, fire and pest hazard; give the kids a chance to claim and somehow re-home anything they legitimately can ("It's my toy Mum and I'm giving it to charity"); and, make it quicker for you / the DC to sort the STUFF should the need or opportunity arise.
Beyond that who knows. Frankly I'm as pessimistic as everyone else, I'm mid fifties and seen too much. I just thought, "If I could think of something helpful which might limbo under the conflict barrier, what would it be?".
Full disclosure - am not a pathological hoarder but find it difficult to throw things out and I kind of feel an echo of the panic and resistance to getting rid. Look into my childhood and - bingo - divorce; bereavement; loss; being given all my stuff in binbags when my mum and stepdad moved house and I was in my final year of uni... nothing big, nothing truly awful, but enough that I cling to things because the people are gone. Significantly, when I managed to get back in touch with my childhood friend, I then threw out 95% of the exercise books from school that I still had in my thirties.