Things might be ok on the host, but not in the hass.io Docker container. One option would be to install Portainer on the host (in it’s own container). Then in the Portainer web interface you can connect to the hass.io container to try connectivity there.
I had a similar problem where my host was also running a DNS server (Dockerised pihole). Other containers on the same host couldn’t do DNS lookups, so nothing much worked. I had to run those containers with --dns=127.0.0.1 (or similar).
I had the same issue. Taking the hint from Ronnie, I checked to see if it was a network issue and was surprised when I couldn’t resolve outside addresses. Home Assistant was using my router as a DNS server (which should have worked), however, I changed it to use Google’s DNS instead (8.8.8.8) and that fixed it.
I changed it by editing the /etc/resolv.conf file but it’s likely that I’ll have to do it again as Network Manager will probably overwrite it unless I use nmcli.
Using nmcli:
nmcli con edit “HassOS default”
set ipv4.dns 8.8.8.8
save
quit