So you're "mostly" eating processed crap with the burgers and not much complete protein. Good luck with that. Try making each meal vegetable-based, with a healthy fat source, some good carbs, and a complete protein... instead of eating carb-based with whatever vegetables and protein happen to fall into it.
Lacto-ovo vegetarianism (allowing for eggs and dairy) can be perfectly fine for building muscle and strength. That's been proven for decades. But anything more animal-free than that and you tend to run into problems getting enough high-quality protein and often getting too many carbs and/or fats, which is why the skinny/skinny-fat vegetarian stereotype is a thing.
Just like with an omnivorous diet, fix your solid food plan before playing around with supplements.