on archlinux I found them in $ENV:XDG_DATA_DIRS

so for $env:LOCALAPPDATA you can

 $IsWindows ? $env:LOCALAPPDATA : $ENV:XDG_DATA_DIRS.Split([IO.Path]::PathSeparator).where({ $_ -like "*local*"})[0]

which returns /usr/local/share on linux

you can do workarounds like these :)