Even for Google logins, would you consider using a token-based authentication system (like Spotify, Postman, etc. do)... i.e., your default browser opens, Google logs you in there (or you already are), and that sends a backend auth token to your service to connect your Google and Replay accounts.
I would like to try your product, but am wary of typing in my Google credentials into an unknown, black-box browser. It's too easy to MITM, especially if someone redistributes a copy with a keylogger shimmed in.
The token-based auth means you can still log in with Google but never have to share your Google password with the proprietary Replay browser. Probably many of the multi-login vendors support something similar already if you don't want to deal with it yourself.