VPN server error - but (I think) I don't have a VPN!

If there is something fishy going on, on your machine, perhaps you might find it by launching Activity Monitor and filtering the list for anything related to VPN.

However, to me, the message sounds more like your Mac is actually trying to connect to a VPN server somewhere, but is unable to, because the server is not responding.

It is possible that you may have installed some software package which for some reason requires connecting to a VPN server.

Do you by any chance use any kind of software which tries to hide your IP address?

I am not familiar with that software, but from the sound of it, I would say "yes". Do you have any monitoring software installed, such as Little Snitch? It could easily tell you if Avira Security is trying to make any surreptitious connections.

An encrypted connection usually means that the data being sent and received is encrypted, but I could see how a VPN might play into the picture as well.

You are welcome, my friend. Glad to have helped.

BTW, I just took a quick look at their page, and I think that gives us a pretty clear answer:

Avira Phantom VPN

Our virtual private network (VPN) lets you securely and anonymously surf the web, and bypass any geo-restrictions or censored websites.

https://www.avira.com/en/free-security-suite

Just a friendly tip. Don't install junk on your Mac. See: Effective defenses against malware and ot… - Apple Community