Now, to the actual functionality test on Focal:

Focal is an LTS release still supported, so messages about esm-apps will be present in MOTD by default.
After creating the marker file and triggering an update of MOTD, those messages disappear, but the updates count remains.

root@focal-sut:~# apt policy update-notifier-common
update-notifier-common:
  Installed: 3.192.30.19
  Candidate: 3.192.30.19
  Version table:
 *** 3.192.30.19 500
        500 http://archive.ubuntu.com/ubuntu focal-proposed/main amd64 Packages
        100 /var/lib/dpkg/status
     3.192.30.17 500
        500 http://archive.ubuntu.com/ubuntu focal-updates/main amd64 Packages
     3.192.30 500
        500 http://archive.ubuntu.com/ubuntu focal/main amd64 Packages
root@focal-sut:~# run-parts /etc/update-motd.d/
Welcome to Ubuntu 20.04.6 LTS (GNU/Linux 6.5.0-21-generic x86_64)

 * Documentation:  https://help.ubuntu.com
 * Management:     https://landscape.canonical.com
 * Support:        https://ubuntu.com/pro

  System information as of Fri Mar 15 22:55:55 UTC 2024

  System load:           1.56
  Usage of /home:        unknown
  Memory usage:          0%
  Swap usage:            0%
  Temperature:           86.0 C
  Processes:             30
  Users logged in:       0
  IPv4 address for eth0: 10.46.74.13
  IPv6 address for eth0: fd42:f539:1893:d366:216:3eff:fe2a:1d97

 * Strictly confined Kubernetes makes edge and IoT secure. Learn how MicroK8s
   just raised the bar for easy, resilient and secure K8s cluster deployment.

   https://ubuntu.com/engage/secure-kubernetes-at-the-edge

Expanded Security Maintenance for Applications is not enabled.

17 updates can be applied immediately.
To see these additional updates run: apt list --upgradable

Enable ESM Apps to receive additional future security updates.
See https://ubuntu.com/esm or run: sudo pro status

New release '22.04.3 LTS' available.
Run 'do-release-upgrade' to upgrade to it.


root@focal-sut:~# touch /var/lib/update-notifier/hide-esm-in-motd
root@focal-sut:~# rm /var/lib/update-notifier/updates-available 
root@focal-sut:~# apt update
Hit:1 http://archive.ubuntu.com/ubuntu focal InRelease
Hit:2 http://security.ubuntu.com/ubuntu focal-security InRelease
Hit:3 http://archive.ubuntu.com/ubuntu focal-updates InRelease
Hit:4 http://archive.ubuntu.com/ubuntu focal-backports InRelease
Hit:5 http://archive.ubuntu.com/ubuntu focal-proposed InRelease
Reading package lists... Done
Building dependency tree       
Reading state information... Done
17 packages can be upgraded. Run 'apt list --upgradable' to see them.
root@focal-sut:~# run-parts /etc/update-motd.d/
Welcome to Ubuntu 20.04.6 LTS (GNU/Linux 6.5.0-21-generic x86_64)

 * Documentation:  https://help.ubuntu.com
 * Management:     https://landscape.canonical.com
 * Support:        https://ubuntu.com/pro

  System information as of Fri Mar 15 22:56:49 UTC 2024

  System load:           1.86
  Usage of /home:        unknown
  Memory usage:          0%
  Swap usage:            0%
  Temperature:           76.0 C
  Processes:             30
  Users logged in:       0
  IPv4 address for eth0: 10.46.74.13
  IPv6 address for eth0: fd42:f539:1893:d366:216:3eff:fe2a:1d97

 * Strictly confined Kubernetes makes edge and IoT secure. Learn how MicroK8s
   just raised the bar for easy, resilient and secure K8s cluster deployment.

   https://ubuntu.com/engage/secure-kubernetes-at-the-edge

17 updates can be applied immediately.
To see these additional updates run: apt list --upgradable

New release '22.04.3 LTS' available.
Run 'do-release-upgrade' to upgrade to it.


I am marking this bug verification-done on Focal.