Comment 2 for bug 1977493

First of all I assume there was no previous attempt of doing a 'do-release-upgrade' or even an attempt that was stopped/interrupted, or an attempt to get the system updated in a different way, for example (in the abs. not recommended way to) to change all 'impish' entries in /etc/apt/sources.list to jammy or so.

Launchpad (https://launchpad.net/ubuntu/+source/pam/) clearly shows that
21.10/impish has currently 1.3.1-5ubuntu11 (and 22.04/jammy has 1.4.0-11ubuntu2).
A different way to check this is:
$ rmadison --arch=s390x libpam-modules | egrep "impish|jammy"
 libpam-modules | 1.3.1-5ubuntu11 | impish | s390x
 libpam-modules | 1.4.0-11ubuntu2 | jammy | s390x
(And since no 'impish-updates' line is listed here, this particular package was also never updated during the impish release.)

So since your current system is (still) 21.10, it must have version 1.3.1-5ubuntu11 installed.
$ lsb_release -cs
impish
$ apt-cache policy libpam-modules
libpam-modules:
  Installed: 1.3.1-5ubuntu11
  Candidate: 1.3.1-5ubuntu11
  Version table:
 *** 1.3.1-5ubuntu11 500
        500 http://ports.ubuntu.com/ubuntu-ports impish/main s390x Packages
        100 /var/lib/dpkg/status
... but I must not have 1.4.0-11ubuntu2 installed, since this is the version of the 22.04 release.

Calling 'apt-cache policy libpam-modules' on your system will give a hint where the currently installed version was taken from.
Sharing the output of this command from your system would be interesting - in addition to the 'sudo apt update' and 'lsb_release -a' output and the file /etc/apt/sources.list.

Such a situation could have been caused if someone downloaded the jammy version of a package manually and (forcefully) installed it
or if someone wanted to try packages from a different release and added an archive line pointing to that different Ubuntu release (e.g. jammy) to the /etc/apt/sources.list file.

The line "'1 upgraded, 0 newly installed, 0 to remove and 1208 not upgraded." is also very suspicious, because 1208 must be close to the overall number of packages in your system (a default install on s390x has about 1020 packages).

So please check that no packages are taken from an Ubuntu release other than the currently installed one:
$ lsb_release -cs
impish
Means check the content of /etc/apt/sources.list (and maybe further sources* files in that folder).
You should also monitor the output of 'sudo apt update' while updating the package indices and check if a wrong Ubuntu release is listed.

In case a wrong archive line is listed, fix it by editing the file and execute:
$ sudo apt clean && sudo apt update
If everything is fine now, upgrade the current system to the very latest level:
$ sudo apt full-upgrade # or maybe: apt dist-upgrade
before re-doing the 'do-release-upgrade'.

(IF a previous do-release-upgrade broke, or an attempt was made to upgrade the system in a different way, the system might be in a pretty bad shape and difficult to fix.
And 'sudo apt-get install --fix-broken' might be needed or even a forceful remove of a wrong package.
Hence, as long as you have access to this system, backup any important data!)