I didn't realise you are listening to your music through a separate amp. A mixer isn't a bad idea, if you don't mind the cost.Yeah I’m thinking the way forward is splitting the 3.5mm headset connection into mic and phones with an adapter. Get an external mic and some sort of mixer for outputs from amp an PC.
One other idea, you can also get microphones with a 3.5 mm connector. There should be a 3.5 mm mic input on your computer and I doubt that this would be blocked.
Corporate W10 laptop here, with a Nobsound amp via USB into Toa NFM's, using the laptop mic too so no headset. Spotify seems to mute connectly when a call comes in. That said, Zoom and Teams seem to be well behaved with respects settings but Skype keeps resetting itself and I have change back manually to Custom after each Skype call.
The work PC is very locked down and the IT policy draconian. I don't even use it to access the internet if I can avoid it. So using a separate source for music is best for me. I think the laptop would accept some of the more basic USB headsets but that does mean swapping headphones. I'd like to mix the two sources so I can hear the Skype ring then at the push of a button mute the music.If you have to run Citrix on your PC are you automatically precluded from running a streamer or listening to music via Radio Paradise or similar?
Alexa for me too.