Discounted price and purchase prompt on iOS App Store
I have this same problem on an iPad.
If I uninstall the app I'm able to install the new version - but like you there are 10 apps I have this same problem with.

My suspicion is that these apps were installed when the iPad was setup to use Apple Account "A". A number of weeks ago I switched the Apple Account of the device to be account "B". So I think the problem is that the app store is preventing an app, installed by "A", being upgraded (for free) by "B".

Is anyone able to confirm this hypothesis?

UPDATE: Yes, this was my problem. I used the old account within the App Store and I was able to update those 10 apps.