As far as I know wine is still only 32-bit and will not work under macOS 10.15.x.
Codeweavers is the developer to follow (news on updates at https://www.codeweavers.com/about/blogs/tag:wine ).
And yes, imho we need a native macOS client to get ride of the wine dependency.
I have a client written in GO that I have compiled for "Darwin 64-bits". I do not have any access to a MAC to test it, nor do I know how you would go about configuring the MAC/browser to respond to sqrl:// . You are welcome to be the first to try it. This client is intended for use by SQRL "Techies" not the average user. You can use the ReadMe files for Windows and Linux to get started.
I can confirm that sqrld (d for Darwin!), from you google drive, works as a "Techies" way (using the Teminal.app CLI ) to log in to this forum with Safari on macOS 10.14.6 (I have not yet updated to 10.15.x)