I had to change the script a bit to be able to launch a xenial lxd vm. Here are the results:

# Testing series xenial
###########################################
Creating xenial-2067810
Device config added to xenial-2067810
Waiting for container IP
Waiting for container ssh
Connection to 10.0.102.82 22 port [tcp/ssh] succeeded!
Waiting for cloud-init to be done
timeout: unrecognized option '--verbose'
Try 'timeout --help' for more information.
cloud-init status --wait failed on container xenial-2067810

dpkg-preconfigure: unable to re-open stdin: No such file or directory

# Latest u-a-t is installed
###########################################
ubuntu-advantage-tools:
  Installed: 32.3~16.04
  Candidate: 32.3~16.04
  Version table:
 *** 32.3~16.04 500
        500 http://archive.ubuntu.com/ubuntu xenial-updates/main amd64 Packages
        100 /var/lib/dpkg/status
###########################################


# Creating conditions for the bug
###########################################
###########################################


# Reproducing the bug
###########################################

# Triggering apparmor DENIED messages
###########################################

# aa-exec -p ubuntu_pro_esm_cache//dpkg dpkg --print-foreign-architectures

# dmesg:
[Fri Jun 21 21:45:19 2024] audit: type=1400 audit(1719006320.072:25): apparmor="DENIED" operation="open" profile="ubuntu_pro_esm_cache//dpkg" name="/var/lib/dpkg/arch" pid=2471 comm="dpkg" requested_mask="r" denied_mask="r" fsuid=0 ouid=0

# aa-exec -p ubuntu_pro_esm_cache apt-cache policy | head
Package files:
 100 /var/lib/dpkg/status
     release a=now
 500 http://security.ubuntu.com/ubuntu xenial-security/multiverse amd64 Packages
     release v=16.04,o=Ubuntu,a=xenial-security,n=xenial,l=Ubuntu,c=multiverse,b=amd64
     origin security.ubuntu.com
 500 http://security.ubuntu.com/ubuntu xenial-security/universe amd64 Packages
     release v=16.04,o=Ubuntu,a=xenial-security,n=xenial,l=Ubuntu,c=universe,b=amd64
     origin security.ubuntu.com
 500 http://security.ubuntu.com/ubuntu xenial-security/restricted amd64 Packages

# dmesg:
[Fri Jun 21 21:45:20 2024] audit: type=1400 audit(1719006321.448:26): apparmor="DENIED" operation="open" profile="ubuntu_pro_esm_cache//dpkg" name="/var/lib/dpkg/arch" pid=2478 comm="dpkg" requested_mask="r" denied_mask="r" fsuid=0 ouid=0
[Fri Jun 21 21:45:20 2024] audit: type=1400 audit(1719006321.452:27): apparmor="DENIED" operation="open" profile="ubuntu_pro_esm_cache//dpkg" name="/var/lib/dpkg/arch" pid=2479 comm="dpkg" requested_mask="r" denied_mask="r" fsuid=0 ouid=0

# esm-cache.service test
###########################################

# /var/lib/apt/periodic/ contents
###########################################
total 8
drwxr-xr-x 2 root root 4096 Jun 21 21:45 .
drwxr-xr-x 6 root root 4096 Jun 21 21:45 ..

# systemctl start esm-cache.service

# dmesg:


# Updating to proposed
###########################################
deb http://archive.ubuntu.com/ubuntu xenial-proposed main
dpkg-preconfigure: unable to re-open stdin: No such file or directory
ubuntu-advantage-tools:
  Installed: 32.3.1~16.04
  Candidate: 32.3.1~16.04
  Version table:
 *** 32.3.1~16.04 500
        500 http://archive.ubuntu.com/ubuntu xenial-proposed/main amd64 Packages
        100 /var/lib/dpkg/status
     32.3~16.04 500
        500 http://archive.ubuntu.com/ubuntu xenial-updates/main amd64 Packages

# Now there must be no apparmor DENIED messages
###########################################

# Triggering apparmor DENIED messages
###########################################

# aa-exec -p ubuntu_pro_esm_cache//dpkg dpkg --print-foreign-architectures

# dmesg:


# aa-exec -p ubuntu_pro_esm_cache apt-cache policy | head
Package files:
 100 /var/lib/dpkg/status
     release a=now
 500 http://archive.ubuntu.com/ubuntu xenial-proposed/main amd64 Packages
     release v=16.04,o=Ubuntu,a=xenial-proposed,n=xenial,l=Ubuntu,c=main,b=amd64
     origin archive.ubuntu.com
 500 http://security.ubuntu.com/ubuntu xenial-security/multiverse amd64 Packages
     release v=16.04,o=Ubuntu,a=xenial-security,n=xenial,l=Ubuntu,c=multiverse,b=amd64
     origin security.ubuntu.com
 500 http://security.ubuntu.com/ubuntu xenial-security/universe amd64 Packages

# dmesg:


# esm-cache.service test
###########################################

# /var/lib/apt/periodic/ contents
###########################################
total 8
drwxr-xr-x 2 root root 4096 Jun 21 21:45 .
drwxr-xr-x 6 root root 4096 Jun 21 21:45 ..

# systemctl start esm-cache.service

# dmesg:

TEST SUCCEEDED