Calm down. I'll explain myself.
What I'm trying to tell you is an opinionated way to build an SPA with a PHP Laravel backend; Supposedly very fast.
Well let's roll that back. Shall we? ⏪
Let's Drop the API part, so we have Laravel and InertiaJs with React, Vue or any other of your choice.
Now Tush up your SPA Authentication with everything Fortify has to offer by using Fortify UI.
Fortify gives you the prebuilt authentication pages in all their raw glory. No styling and confusion.
All you have to do is follow it's lead. Create your components, and post your forms to the same routes used in FOrtify UI's views.