The sessions spec says:

ClientSession instances are not thread safe or fork safe. They can only be used by one thread or process at a time.

*Drivers MUST document the thread-safety and fork-safety limitations of sessions.* Drivers MUST NOT attempt to detect simultaneous use by multiple threads or processes (see Q&A for the rationale).

It does not appear that we document this in Python. We should document this in start_session and in ClientSession.