Eloquent does not use Doctrine. It only optionally uses Doctrine DBAL for some advanced migrations, but isn’t required otherwise.
You can use Blade and Twig together in your application, but you can’t mix the two in your templates. So you could probably create your base template in both Twig and Blade and then switch out your templates one by one. Or only change your front-end to Twig and keep Blade in the back-end etc.