Definitely this. Flask is old and well-tested, with a solid feature set and little need to change how it works.
Also you'd use Flask for basically anything that isn't an "API", but where you still want something lighter-weight than Django. I believe other traditional Python web frameworks like Pyramid fall into the same category.
The "Fast" in FastAPI refers to the speed of getting a working prototype running, specifically for an API that accepts and emits JSON and implements an OpenAPI schema. If that's not your use case, then you might not need or want FastAPI.
Also you'd use Flask for basically anything that isn't an "API", but where you still want something lighter-weight than Django. I believe other traditional Python web frameworks like Pyramid fall into the same category.
The "Fast" in FastAPI refers to the speed of getting a working prototype running, specifically for an API that accepts and emits JSON and implements an OpenAPI schema. If that's not your use case, then you might not need or want FastAPI.