So, this is set somewhere in your config files, I think. Maybe try:

grep -r SSH_AUTH_SOCK /etc
grep -r SSH_AUTH_SOCK ~/.*

Just to see where it’s being set.

What happens if you do:

unset  SSH_AUTH_SOCK

And then try to connect?

Can you post the result of the env command as well? It sounds like your config is very minimal, but the fact that it’s looking for a local Unix socket in the strace output is weird.