Why does it being WebAPI-exposed interface matter at all then? It is an extremely confusing way of phasing it. It literally doesn't matter, and even reading back if that IS what they meant then it is still a really circular way of wording it.
Most likely they're referring to the C# part being written for Microsoft's "ASP.Net Web API" framework, rather than just being a web API in general.
That framework is designed for C# programmers and most of the resources (tutorials/stackoverflow answers/etc) around it will assume you are writing C#. So it makes some sense to use C# for that part of your application even if most of the underlying business logic is implemented in separate F# libraries.
That's probably why they specified it - to explain why they're using both C# and F#. I can see how it could be confusing, especially if you're not familiar with that rather generically named framework.
It doesn't. That was just an incidental piece of detail.
If it makes it more comfortable to you, replace "WebAPI" with any other technology that interfaces your code with the outside world. Maybe a UI toolkit or something.