Many fireworks are designed to explode at altitude. The biggest risk is probably if the firework is ingested into an engine (also a major risk for bird strikes).
Given the sheer quantity of energy that's already being continuously released in an engine would a small firework actually pose more danger than a bird? There's no bones in a firework after all.
Even small bird strikes are usually a non-event, as the engines are designed to withstand them (there's a very well-known YouTube video of frozen chickens being fired into one, and those are already a lot bigger and harder than most birds they'll encounter.) It's the big ones that make the news.