Trying the new Inkscape 1.3 as appimage, I used "./Inkscape-0e150ed-x86_64.AppImage --appimage-mount" to mount the image as root, and that seems to succeed with message "/tmp/.mount_InkscaYEqRgu".

However when I try to access that directory from another terminal I only get "permission denied, even for "ls -d":
> ll /tmp/.mount_InkscaYEqRgu
ls: cannot access '/tmp/.mount_InkscaYEqRgu': Permission denied
> ll -d /tmp/.mount_InkscaYEqRgu
ls: cannot access '/tmp/.mount_InkscaYEqRgu': Permission denied

Oddly, the directory exists, because I can access it as root:
# ll /tmp/.mount_InkscaYEqRgu
insgesamt 100
-rwxr-xr-x 1 root root  3075 21. Jul 14:26 AppRun
-rw-r--r-- 1 root root 40270 21. Jul 14:27 .DirIcon
drwxr-xr-x 5 root root     0 26. Mai 16:05 etc
drwxr-xr-x 4 root root     0  8. Jul 2021  lib
drwxr-xr-x 2 root root     0 21. Jul 14:27 lib64
-rw-r--r-- 1 root root 19274 21. Jul 14:27 org.inkscape.Inkscape.desktop
-rw-r--r-- 1 root root 40270 21. Jul 14:26 org.inkscape.Inkscape.png
drwxr-xr-x 6 root root     0  8. Jul 2021  usr

The problem seems to be this (from stace):
statx(AT_FDCWD, "/tmp/.mount_InkscaYEqRgu", AT_STATX_SYNC_AS_STAT|AT_SYMLINK_NOFOLLOW, STATX_MODE|STATX_NLINK|STATX_UID|STATX_GID|STATX_MTIME|STATX_SIZE, 0x7fff110a3fb0) = -1 EACCES (Permission denied)

When trying to use the appimage as non-root, it won't work either:
> ./Inkscape-0e150ed-x86_64.AppImage 
fuse: failed to exec fusermount: Permission denied

Cannot mount AppImage, please check your FUSE setup.
You might still be able to extract the contents of this AppImage 
if you run it with the --appimage-extract option. 
See https://github.com/AppImage/AppImageKit/wiki/FUSE 
for more information
open dir error: No such file or directory