I can’t update but I can install apps (App Store)
It is possible that the developer has changed the bundle-ID of the application, which essential makes it a completely new app - just with the same name. This could explain why you cannot update your app that has the old bundle-ID, whereas other user's who downloaded the newer app with the new bundle-ID can.
This can happen for example when a company that owns an app sells that app to another developer. In certain cases, they need to use a new bundle identifier.