Dietpi-banner does not display 'update available' messages

Which error?

That would be a massive overhead. Also, it wouldn’t achieve what you might think, since the update check of course has not finished yet when the banner is shown. … I mean you could trigger it as foreground task via /etc/bashrc.d ordered before dietpi.bash, which shows the banner. But then you would need to wait for the update check + in case APT update check on every single login, before the command prompt appears.

If it really is important for you to see available updates ASAP after a reboot, and if it is a headless system, you can order dietpi-postboot.service to start after time-sync.target. But check whether chrony.serviceis pulling in and sorts itself before time-sync.target, else this wouldn’t have much meaning. If not, there is a systemd-time-wait-sync.service, which primarily waits for systemd-timesyncd.service to finish the actual sync (just like our run_ntpd), but its manpage states that it works with other time sync daemons as well, just not as reliable: systemd-time-wait-sync(8) — systemd-timesyncd — Debian trixie — Debian Manpages

I’m finding it difficult to describe the error at the moment, as there isn’t currently a DietPi update available.
From memory, I can only say that dietpi-update crashes, retrying doesn’t help, so I terminate the process myself and restart it, and then it suddenly works.
Should it happen again, I’ll get in touch.
I can’t describe it any better than that at the moment.
Despite having used DietPi and Linux for years, I’ve never delved into the depths of the system.
That’s precisely why I enjoy using your extremely user-friendly OS so much.

I’ll follow your advice and give up on my desire to see a current list of available updates every time I log in via SSH to my headless systems.
The effort involved, the benefits and the practicality of it all don’t really seem to be worth it.
Nevertheless, many thanks for the detailed explanations.