BufferedIOBase is an abstract class and, despite the name, doesn’t necessitate a buffer or cache. Adding methods and properties might break compatibility with third-party implementations, or get ugly with optional methods and multiple versions of the API. It seems like it would be better to extend the concrete APIs: io.BufferedReader, BufferedWriter and/or FileIO.
In Issue 32475 there is a proposal to add a “getbuffn” method returning the amount of unread pending data in a reader object. Perhaps that would be enough for reading.
I would support an similar API for BufferedWriter etc. Perhaps a property called “available_space”. You could check that and decide whether to do a direct non-blocking “write”, or launch a blocking “write” in the background.