This problem has been reported in the Core and Supervisor repos but still awaiting an official response. Perhaps someone in the community has some idea what’s the cause (and the remedy).
Here’s the Supervisor log after attempting to update from 2022.4.1 to 2022.4.5 (same result with 2022.4.6).
22-04-20 12:02:27 INFO (MainThread) [supervisor.homeassistant.core] Updating Home Assistant to version 2022.4.5 22-04-20 12:02:27 INFO (SyncWorker_3) [supervisor.docker.interface] Updating image ghcr.io/home-assistant/raspberrypi3-homeassistant:2022.4.1 to ghcr.io/home-assistant/raspberrypi3-homeassistant:2022.4.5 22-04-20 12:02:27 INFO (SyncWorker_3) [supervisor.docker.interface] Downloading docker image ghcr.io/home-assistant/raspberrypi3-homeassistant with tag 2022.4.5. 22-04-20 12:02:27 ERROR (SyncWorker_3) [supervisor.docker.interface] Can't install ghcr.io/home-assistant/raspberrypi3-homeassistant:2022.4.5: 500 Server Error for http+docker://localhost/v1.41/images/create?tag=2022.4.5&fromImage=ghcr.io%2Fhome-assistant%2Fraspberrypi3-homeassistant&platform=linux%2Farm64: Internal Server Error ("Get "https://ghcr.io/v2/": dial tcp: lookup ghcr.io on [::1]:53: read udp [::1]:43736->[::1]:53: read: connection refused") 22-04-20 12:14:34 WARNING (MainThread) [supervisor.homeassistant.core] Updating Home Assistant image failed
I may be interpreting the error message incorrectly but it seems to suggest a DNS problem while performing a lookup.
Running on RPi3 with Home Assistant Supervised on Debian. Had no problem upgrading to 2022.4.1. DNS is local and hasn’t changed since the upgrade to 2022.4.1.
me@ha:~$ ha dns info host: 172.30.32.3 locals:  servers: - dns://192.168.1.2 update_available: false version: 2021.06.0 version_latest: 2021.06.0