That's the crux of the question. The BFF approach says that you remove logic from the client and put it in a server-side component. Not that you add extra logic. Then you might find that you need to copy that server-side component sideways for a new client, if the view layer in that client is sufficiently different to what you already have. The browser can be the only client of its BFF API; the mobile apps can either speak to the same API or have their own.

Dramatically more important than any theoretical, abstract consideration in deciding whether this can work is what your teams look like. The client team should almost certainly own the BFF API, which has implications for skillsets and maturity.