Please provide more details with use cases.

Are these media files for products?

One solution that comes to mind, you can name your files (or title) beginning with something that is unique to the group. You can search for that group.

There is no ability to create categories for media files. We can consider adding categories, but there might be more to it and we need to discuss details. 

Sounds like you need to generate unique token/id for your download and encode it to QR code with the link.
This entirely custom process, as I see it, would consist of 2 parts.

1. Backend process or admin that will generate QR code for given customer/download
2. Frontend controller (based on URL in QR code) to validate the token and provide download.

New version of AbanteCart 1.3.1 is now released.

Master branch is set to be 1.3.1.
https://github.com/abantecart/abantecart-src

New Features and improvements highlight:
https://github.com/abantecart/abantecart-src/releases/tag/1.3.1

What is a version of AbanteCart and PHP?

Hello timlight10,

I just tried really quick with ElasticCloud and it works for me.
If you still struggle, please contact extension support with the access to your admin.

Good luck

Hello Huijun,

See if this helps you
https://forum.abantecart.com/index.php?topic=6258.0