screen sharing of e.g. a YouTube video does only show the video, but not the audio

Hello to all, I'd like to ask you for some help:

Typically, as a host, I like to use a headset for Zoom calls. That works fine - except: when I want to present e.g. a YouTube video, then I do only get the video information, but without the audio.

It's obvious that this is not a practical way.

But as soon as I switch off the headphone , i.e. using the (quite lousy) acoustics in my office, the audio catches in. But it seems, that the micro of my external camera does simply transmit the audio here in the office, means, that the audio is taken to the Zoom call via the output of the speakers.

I would expect that the audio signal would be transmitted to the Zoom call "internally".

Please, what do I need to do for having the full YouTube clip as a shared resource whilst using my headset?

Thanks in advance !