Correct way to handle email/password sign up, in addition to using Laravel Socialite for OAuth?

Question

I'm building an iOS app with Laravel backend.

I'm using Firebase Authentication to handle the following authentication types: Google, Apple, and email/password sign up.

I've set up Google and Apple sign up by utilizing Laravel Socialite, however it doesn't look like Socialite supports an email/password driver, so I can't use this code for email/password authentication:

class AuthController extends Controller
{
    public function login(Request $request)
    {
        $validator = Validator::make($request->all(), [
            'provider_name' => 'required|string|in:google,apple',
            'access_token' => 'required|string',
        ]);
 
        if ($validator->fails()) {
            Log::info($validator->errors());
            return;
        }

        $providerName = $request->input('provider_name');
        $token = $request->input('access_token');

        $providerUser = Socialite::driver($providerName)
            ->userFromToken($token);

        $user = User::where('provider_name', $providerName)
            ->where('provider_id', $providerUser->id)
            ->first();

        if ($user == null)
        {
            $user = new User;
            $user->name = $providerUser->name;
            $user->email = $providerUser->email;
            $user->provider_name = $providerName;
            $user->provider_id = $providerUser->id;
            $user->save();
        }

        $token = $user
            ->createToken("token")
            ->accessToken;

        return response()->json([
            "status" => "success",
            "data" => [
                "token" => $token,
                "user" => $user
            ],
        ]);
    }
}

So what's the "right" way of ALSO handling email/password sign up?

I'm at the point where I've the user is signed in on the iOS app and the account has been created through Firebase. I just don't know what to do to actually pass the user data to the Laravel backend and handle authentication/tokens as I do with Google/Apple authentication.