Is it just me or is the yok in the audio barely audible?
Yes, it's a bit faint. It might be a TTS thing, but it's also very common in Turkish to drop the voice towards the end. So, heads up for that.
It happens in a lot of the sentences on Duolingo, which can make getting the some of listening exercises correct very difficult.
I did not hear it either.
Why is it not 'even the doctor's not at the hospital'?
Why is "At the hospital there is not even a doctor" wrong?