Okay guys,
first things first - I found the problem!
I thought networking can't be the issue, because of the working 0.48 version - but I was wrong.
I don't know why, but after starting 1.16.1 I have allowed Windows everything for the firewall-settings via the windows defender dialog. After posting my last answer, I jumped into the windows defender firewall settings and checked for incoming rules.
From 6 saved rules, two rules were set to NOT ALLOWED. I have double-checked all entries and changed the two NOT ALLOWED entries to ALLOWED.
My browser automatically refreshed and detected the 1.16.1 server and connected instantly.
So sorry for my weird issue. I had that not in mind at all! Hopefully someone finds help in this thread, when he runs into same problems.
Thanks a lot,
Kai