Hello,
I don’t see problem with the Product categories count:
Backend – https://prnt.sc/wmh6dm
Frontend – https://prnt.sc/wmh6lg
Filter by material
backend – https://prnt.sc/wmh72o
frontend – https://prnt.sc/wmh7ck
Out of stock displays the wrong number, you are right. I have passed this issue to our develoeprs.
Regards