Alright, I have just launched the test in a VM containing Win 10 v21H2 and I'm affirmative:
Skype app from Microsoft Store is able to add item in context menu without needing to reboot computer (or reopening Windows session). The item is "Share with Skype" as shown below:
Let me reiterate my previous request:
Please mention Menu extension works only after Windows session reopening until this bug is fixed.