So Microsoft decided to deploy a new version from the Microsoft Store.

There were a couple of reasons given:
Kapil Tundwal - The reason we chose Microsoft Store is because it allows us to send security updates faster.

or was it because of Skype for Business deprecation?
MrShannon - Apps can trigger a WebView2 install, but non-admins would still be unable to do that. The UAC prompt is actually not due to WV2, it's because of the UIAccess capability that is required for a 'modern app' in its manifest. The 'choice' was forced because of the SfB deprecation

Of course there were some problems with the Microsoft Store version of Quick Assist:
Not impressed - why not just update the existing app? - users need admin rights to install the new one - existing shortcuts stop working - users now have 2 apps when they search - have any of you (MS) actually tried talking a user through all this on the phone???

Admin Rights?
Kapil Tundwal - Why do users need admin rights to install a new app? Quick Assist store app allows helpers to take full control of user's device. We think it's important for users to be in control of what gets installed on their device from a security and privacy perspective.
(So when the new version gets installs, it needs Admin Rights to uninstall the old version.  In Corporate IT, we don’t let users have Admin Rights…)

Existing shortcuts stop working / end users now have 2 Quick Assist apps
Kapil Tundwal: Thx for feedback Scott. I am Engineering Manager of Quick Assist app. We found out this bug shortly after releasing it. We have fix on the way. v2.0.6.0 is flighted right now which will remove shortcut to old app. We also plan to update inbox app through windows update
(So Microsoft’s thinking seems to be “Let’s continue breaking end users.  But we do have a fix coming”)

So how do I fix it?
Mr Shannon has a great blog post over here, detailing what you need to do.