Asyncio weird behaviour

[vugz]

I am having difficulties understanding the output of the following program

import asyncio

async def inner():
    try:
        print("Inside inner")
        await asyncio.sleep(3)
        print("Awaken inner")
    except asyncio.CancelledError:
        print("Caught cancel exception in spawner")

async def main():
    try:
        a = asyncio.create_task(asyncio.wait_for(inner(), timeout=2.0))
        await a
    except asyncio.TimeoutError:
        print("Timeout")

    await asyncio.sleep(5)

asyncio.run(main())

The output is

Output:
Inside inner
Caught cancel exception in inner

I undestand that this might be because I am not familiar with the inner details of asyncio, as I don't really understand what are Futures and such.

What I think is happening:
We create a task which is the wait_for coroutine wrapping the inner coroutine. From my little understanding I expected that since inner will timeout, wait_for would raise a TimeoutError, however, since wait_for is wrapped in create_task this will no propagate up towards the line await a. Is this assumption correct?
The first time I ran this I expected the output to be

Output:
Inside inner
Timeout
Caught cancel exception in inner

Thank you, I would highly appreciate a more in-depth explanation of what actually happens!