I am having the same issue it seems.
One thing I am noticing with mine is that in the Aki.Server.exe window the client is making these two requests to the server.
[Client Request] /launcher/profile/info
[Client Request] /launcher/server/version
It doesn't seem like the server is responding. So it repeats the request after a few minutes. So if you leave it on the loading screen for awhile you see these two lines over and over again.
I did get the green text of:
Started webserver at http://127.0.0.1:6969
Started websocket at ws://127.0.0.1:6969
Server is running Happy playing!!
So the server should be working just that specific request isn't being received or processed.
