Launch vue3 app from laravel, maintain session

I am working on an application that has two core systems. One is the main laravel app which serves a basic front end & manages all of the backend & API code. The second system is an entirely separate codebase & is a vue3 application. The idea is the LaravelApp will be used as a place to manage & launch the vue app from. All authentication etc. will be managed in the laravel app, then you will be able to launch into this vue app.

What I'm struggling to understand is how I can create it so that you log into the laravel frontend and you click a button that launches into the vue3 app but maintains the same laravel session/auth (Note: the vue3app is not in the laravel codebase).

Can someone give me some pointers on things to google/search for as I keep hitting a brick wall and can't find what I am looking for. I assume it's going to be like a one-time magic login link, is this correct? Any help massively appreciated

The system tldr is as follows: Laravel used as 'admin' side of the vue app. Different users can create an 'organisation'. Then users can launch into that 'organisation' which should be loaded in the vue3 app. But only certain users can view certain organisations. I need to get it so a user can login to the laravel site, then view a list of organisations they are a part of, click 'open' and it opens the vue3 app which automatically sets up all of the auth etc. with no separate login screen