Listing the possibilities…
- DNS configuration on Mac (ruled out, I think)
- Something on router between Mac and the Internet (probably not due to test results)
- ISP shenanigans
- Mail extension
- Browser extension
- Browser settings
- Firewall
- Anti-virus, for example Sophos monitors network connections from browsers
- Certificate issues
Which web browsers do you have installed, besides Safari? I’d suggest changing the default web browser in System Settings, and then try your email test again. If it works, then you’ve narrowed it down to Safari-related.
Also, what do you mean exactly by:
Are you manually entering a different URL than the URL that you’re cutting/pasting?
I’m getting a feeling this is related to URLs being upgraded to https. There’s a policy related to this in Safari or Firefox; I ran into weird problems with this long ago.