Host Doesn't See Container's /run Files

I have a Debian host. I create and start an Alpine container. The Debian host cannot see what is in the container’s /run directory but can see what is in the container’s /tmp directory. Is there something special about the /run directory or is it normal that the host cannot see files in container directories?

root@debian:~# lxc-create -n mycontainer -t download -- -d alpine -r 3.19 -a amd64

root@debian:~# lxc-start -n mycontainer

root@debian:~# ls -alhF /var/lib/lxc/mycontainer/rootfs/tmp
total 16K
drwxrwxrwt  4 root root 4.0K Jan 15 02:34 ./
drwxr-xr-x 19 root root 4.0K Jan 15 02:34 ../
drwxrwxrwt  2 root root 4.0K Jan 15 02:34 .ICE-unix/
drwxrwxrwt  2 root root 4.0K Jan 15 02:34 .X11-unix/

root@debian:~# ls -alhF /var/lib/lxc/mycontainer/rootfs/run
total 8.0K
drwxr-xr-x  2 root root 4.0K Dec  7 09:43 ./
drwxr-xr-x 19 root root 4.0K Jan 15 02:34 ../

root@debian:~# lxc-attach -n mycontainer

~ # ls -alhF /tmp
total 16K    
drwxrwxrwt    4 root     root        4.0K Jan 15 02:34 ./
drwxr-xr-x   19 root     root        4.0K Jan 15 02:34 ../
drwxrwxrwt    2 root     root        4.0K Jan 15 02:34 .ICE-unix/
drwxrwxrwt    2 root     root        4.0K Jan 15 02:34 .X11-unix/

~ # ls -alhF /run
total 20K    
drwxr-xr-x    4 root     root         240 Jan 15 02:34 ./
drwxr-xr-x   19 root     root        4.0K Jan 15 02:34 ../
-rw-r--r--    1 root     root           4 Jan 15 02:34 crond.pid
----------    1 root     root           0 Jan 15 02:34 crond.reboot
-rw-r--r--    1 root     root          38 Jan 15 02:34 ifstate
-rw-------    1 root     root           0 Jan 15 02:34 ifstate.eth0.lock
-rw-------    1 root     root           0 Jan 15 02:34 ifstate.lo.lock
drwxrwxr-x    3 root     uucp          60 Jan 15 02:34 lock/
drwxrwxr-x   14 root     root         340 Jan 15 02:34 openrc/
-rw-r-----    1 root     root           4 Jan 15 02:34 syslogd.pid
-rw-r--r--    1 root     root           4 Jan 15 02:34 udhcpc.eth0.pid
-rw-rw-r--    1 root     utmp           0 Jan 15 02:34 utmp

That’s perfectly normal, /run in your container is its own mount, likely a tmpfs.
It’s not a directory on the persistent rootfs mount.