@thesurreyfriends - Thanks for your help. Here's how it went. Regarding...
You should also be able to download a compatible version of GarageBand for your macOS 12.7.2 in a similar fashion. Drag your current version of GarageBand to the trash but do not empty the trash just yet.
... I tried the above. But then the following instructions did not work...
Open the App Store and click on your name ( also known as your account) bottom left of screen.
This takes you to your Purchased page which should list GarageBand with other applications
such as iMovie etc.
Click on the download symbol and you should be offered to download the latest compatible version for 12.7.2
In this situation you will be offered the version of GarageBand "that matches your installed OS"
... because, if I remember correctly, it did not let me download GB again.
However, I got onto Apple phone support (who were really nice) and, after some head-scratching, they gave me one important different step, which I'll outline here...
Takeaway Tip: Dragging your current version of GarageBand to the trash is not enough (even if you empty the trash!). Mac apps can still persist some information beyond that which can affect attempts to fix a problem by re-installing applications
Instead, the crucial step to take is...
- Open the "Storage Management" app on your Mac, ie.
- Select "Applications" in the left menu of the Storage Management app
- Select Garageband in the list of applications
- Click Delete in the bottom right of the Storage Management app window
- Confirm to Delete in the popup
- This performs a more complete app deletion than moving an app to the trash (or moving app to an external hard disk - which I also tried)
Then, when I tried your final steps...
Open the App Store and click on your name ( also known as your account) bottom left of screen.
This takes you to your Purchased page which should list GarageBand with other applications
such as iMovie etc.
Click on the download symbol and you should be offered to download the latest compatible version for 12.7.2
In this situation you will be offered the version of GarageBand "that matches your installed OS"
... everything worked and I could reinstall Garageband successfully! (without loss of projects... as far as I remember)
Thanks again for you help @thesurreyfriends.