flask-openapi3 looks good but has only 246 stars. Would be worried using it in production. flask-pydantic has no openapi tie-in. Oh look, there's me bumping the openapi request that's been an issue since 2020: https://github.com/pallets-eco/flask-pydantic/issues/17 which has an open PR since 2022.
It's possible between Quart and svcs (for DI) and some Pydantic/Marshmallow/OpenAPI extension you might be able to mimic what FastAPI does. But I'd just use FastAPI. I use async too. It's a lot easier to scale in my opinion.
Do none of these pieces matter to you? Like do you not do any data validation or care about OpenAPI?
Dependency injection in fastapi honestly feels like a horrible afterthought. Flask's g is much easier to reason about, and 99% of projects don't need the 'performance improvements' of async.