You could check the official project generator, it includes a simple Vue.js front end: https://github.com/tiangolo/full-stack-fastapi-postgresql
Although I'm currently using React with TypeScript and hooks, and it's a great development experience. I plan on adding it to the project generator later.
Where I think this could be taken to the next level of reusability is in modularising the front-end into API-specific components. For example, the login behaviour could depend on FastAPI-Users, with a sibling frontend library containing components that implement the same login flow. Adding user behaviour is then a matter of using the same third-party library on the front and back end.
This approach could be extended to other components such as an admin panel (perhaps using https://github.com/awtkns/fastapi-crudrouter), or a blogging component.
But that's also gonna be for whenever I get the time to invest in it :)
Since the design of FastAPI programs is often modular, with libraries and modules extending the API with additional routes, it seems to make sense to build front-end components according to the same module structure. I'm yet to see any of these for popular libraries, but I'd be up for helping build some in libraries like Vue.
Does anyone know of existing projects/server frameworks where backend modules are coupled with front-end components that consume their API?