Is your "<synapse_domain>/.well-known/matrix/client" set up?
We can continue this in the Issues I guess. I noticed there was a planned improvement for error snackbars in the login so that would solve half of the issue. But I found no other issue with problems logging in open right now.
I've added a new ticket linking back to this comment and I'll look into the issue. I have several people using Syphon with their own homeservers successfully so I'm thinking the problem has to do with a silent error that's unrelated. Thanks for the feedback though and feel free to respond in the github issue itself.