Here is the best description I have seen of the problem, from earlier post by ArthurBA
iTunes 12.6.5.3 on Mac cannot download new apps or update existing apps
Recent Similar Reports: Many
Resolution: Open
Product :iTunes for Mac OS before Mojave
Issue: Incorrect/Unexpected Behavior
I've downloaded iTunes 12.6.5.3 for Mac and Windows from here:
https://support.apple.com/en-us/HT208079
The Windows version DOES NOT exhibit this bug.
Since March 19th, the MacOS version cannot download or update iOS apps. Prior to March 19th it worked OK. MacOS High Sierra is the latest version of MacOS that this version of iTunes is supported on (as per the support note above it will not run on Mojave or Catalina).
Install new app fail
1. start iTunes
2. switch to app view
3. click on "App Store" tab.
4. purchase app/get free app (eg: TikTok)
5. window briefly flashes "downloading ..."
6. app is not downloaded
Update fail
1. start iTunes
2. switch to app view
3. click on updates tab
4. click on "Update All Apps" button
5. window briefly flashes "downloading ..."
6. no apps are updated
If the windows version works, and the mac version does not, then the implication is that Apple wants us to use the Windows version and retire our macs. I suspect this was not Apple's intention.