How to update apps on a shared computer?
Solution 1:
This is how applications from Mac App Store work - not how macOS works with applications. That is if you obtain an app from outside the App Store none of this applies.
In broad terms the app is licensed to one person only and they can use the app on multiple devices and only that person can interact with the App Store (e.g. update the app)
Note that from EULA so the wording is not the simple owner of or who "bought" the app.
The Mac App Store Products and App Store Products (collectively, “App Store Product(s)”) made available through the Mac App Store Service and App Store Service (collectively, “App Store Service(s)”) are licensed, not sold, to you.
Apple has set up Mac App Store that applications from it are licensed to the person who pays for the app using their Apple ID
Only the owner of that Apple ID can update the apps etc. However any other user can run them.
If you have multiple users on a machine and want more than one to be able to update them then you have to use a multi user solution which includes Family Sharing and Volume Purchase Programme (no link as the ones I found lead to dead links)
The parts of the App Store EULA that matter here are
This license does not allow you to use the Licensed Application on any Apple Device that you do not own or control, and except as provided in the Usage Rules, you may not distribute or make the Licensed Application available over a network where it could be used by multiple devices at the same time. You may not rent, lease, lend, sell, transfer redistribute, or sublicense the Licensed Application and, if you sell your Mac Computer or iOS Device to a third party, you must remove the Licensed Application from the Mac Computer or iOS Device before doing so.
Thus if you want to have your mother use the apps that you have licensed from Apple then either you need to add her to Family Sharing or if she will be using the computer completely separately away from your control then you need to remove the apps that you have licensed from Apple.