Store doesn't really have a new icon as it seems like it's not updating the icon correctly just like some other apps, if you Add-AppxPackage the newest version in C:\Program Files\WindowsApps, it will restore the correct icon.
Is there such a thing as Updates history in Store? As it seems like you only see the updates when it's being downloaded and updated in Downloads and Updates.
Turn On or Off Automatic Download and Install of App Updates by Microsoft Store app in Windows 10
The Microsoft Store app in Windows 10 offers various apps, games, music, movies & TV, and books that users can browse through, purchase, or get...