Hi, Eunice KX!
Thanks for reaching out to Microsoft Community and posting your inquiry. We understand you wish to focus on work while wearing your Surface Headphones and use the active noise cancelation feature. We are sorry to learn if you constantly get notifications from the connected host devices.
The active noise cancellation feature is designed to block out external sound. To avoid getting notifications from the connected host device, please put the computer/phone into Silent/Mute/Do Not Disturb (DND) mode.
What you're looking for is a great suggestion though. Kindly post this as a feedback via the Feedback Hub app. Visit this page to be guided on how to do so: https://support.microsoft.com/help/4021566/
If this answers your question, please let our Community know by marking this post as an answer. Otherwise, don't hesitate to respond to this thread if there’s anything else that needs to be addressed.
Kind regards,
Janette_Z