Due to how Arch Linux works, I would rather not setup an entire installation image with my exact specifications (It would take a rather long time with my limited system specifications, and creating an image and ripping it of my personal info would take even longer). However, the problem has continued to persist even now. I apologize for the lengthy wait for a response, ended up getting caught up in a lot of stuff over the past few months.
Back to the matter at hand, you may be able to quickly install Arch Linux into Virtualbox. My system is varied quite a bit from stock Arch, but I am using the default kernel, and the
command helps a lot in automating the install process (I used it when I installed Arch onto this machine). Once the system is up and running, I'm simply using the GNOME 40 desktop environment (easily install-able from the
command that is included with arch). From there, you have 90% of what my system is for the most part, the other 10% being simply smaller tweaks that I doubt would be the issue for the sign-in issue.
Come to think of it, it may be a problem with how WINE is interfacing with the internet. I'll play around with some configurations and update with a fix if I come across a solution, for anyone else who may experience this issue.