General API Question

Yes, you are correct. You will need to use a package like PHP-JWT to authenticate the user in the second Laravel application. You can use the JWT package to generate a token when the user logs in to the first application. Then, when the user makes a request to the second application, you can pass the token in the request header and use the JWT package to authenticate the user.

Here is an example of how you can generate a token in the first application:

use \Firebase\JWT\JWT;

$key = "example_key";
$token = array(
    "iss" => "http://example.org",
    "aud" => "http://example.com",
    "iat" => 1356999524,
    "nbf" => 1357000000
);

$jwt = JWT::encode($token, $key);

And here is an example of how you can authenticate the user in the second application:

use \Firebase\JWT\JWT;

$key = "example_key";
$jwt = $_SERVER['HTTP_AUTHORIZATION'];

try {
    $decoded = JWT::decode($jwt, $key, array('HS256'));
    // User is authenticated
} catch (Exception $e) {
    // User is not authenticated
}