I have audacity on my old laptop, not sure of the version but it must be a few years ago, everything works well, I can mute the speaker while I’m recording from you tube and the recording still carries on without problem, I don’t always want to listen to it while I’m recording so this is handy.
However I’ve now got a new laptop and have just downloaded the latest version, I can still record as above but when I mute the speaker the recording also mutes. Iv’e checked the setting between the two and they are the same.
It depends on your drivers and your version of Windows.
You can plug-in external (analog) speakers and turn down their volume knob. or plug-in headphones and stick them in a drawer if you don’t want to hear them at all. Or, sometimes you can plug-in a headphone extension with nothing plugged into the other end (but some laptops will detect nothing connected and keep the speakers playing).
…And don’t complain! You aren’t supposed to steal from streaming services. There’s a reason they don’t give you a handy download button…