I found that keeping the frontend & backend in sync was a challenge so I wrote a script that reads the schemas from the backend and generated an API file in the frontend.
I personally I prefer #3 for its explicitness - you can actually review the code it generates for a new/changed endpoint. It does come w/ downside of more code + as codebase gets larger you start to need a cache to not regenerate the entire API every little change.
Overall, I find the explicit approach to be worth it, because, in my experience, it saves days/weeks of eng hours later on in large production codebases in terms of not chasing down server/client validation quirks.
I'll almost always lean on separate packages for any shared logic like that (at least if I can use the same language on both ends).
For JS/TS, I'll have a shared models package that just defines the schemas and types for any requests and responses that both the backend and frontend are concerned with. I can also define migrations there if model migrations are needed for persistence or caching layers.
It takes a bit more effort, but I find it nicer to own the setup myself and know exactly how it works rather than trusting a tool to wire all that up for me, usually in some kind of build step or transpiration.
Write them both in TypeScript and have both the request and response shapes defined as schemas for each API endpoint.
The server validates request bodies and produces responses that match the type signature of the response schema.
The client code has an API where it takes the request body as its input shape. And the client can even validate the server responses to ensure they match the contract.
It’s pretty beautiful in practice as you make one change to the API to say rename a field, and you immediately get all the points of use flagged as type errors.