I want to use Nuxt.js for my frontend and laravel sanctum as my backend authentication provider. How should I set the SESSION_DOMAIN key in the .env file in my laravel project.
Also should I edit anything in the server object part in the nuxt.config.js file to make this work?
When you use Sanctum with SPA, such as Nuxt, you've the option to use either API or cookies/sessions. If your application is a first-party application on same top level domain, Laravel recommends to use cookie based approach so you can take advantage of CSRF protection. Axios and Angular Http libraries handles CSRF out of the box, so you don't have to worry too much about handling the requests headers [1].
In your case, I assume your application is first party and is on same top level domain. So your SESSION_DOMAIN value would be for example .domain.com. Also you'll need to set SANCTUM_STATEFUL_DOMAINS=domain.com as well. Usually your SESSION_DOMAIN will have just the main domain your application uses on, while SANCTUM_STATEFUL_DOMAINS will have all the subdomains (if any), that your frontend uses.