I've recently been looking into clang's _ExtInt feature (allows you to declare any size int) a lot and was just wondering if there is also an _ExtFloat which I could use to create custom size floats.
No, it does not.
For reference, here is what an LLVM developer stated on Reddit when asked the same question (Source):
We've actually discussed this, but they are incredibly difficult to specify. You need 3 different pieces of information, and they don't scale on different hardware well.
In the case of integers, you can do transitions with truncations/sign extensions, with floats you'd need a large software library to convert floats of unsupported sizes.