Download Big Sur to be installed on old computer on my M2 mini

The Mac mini M2 never shipped with the earlier macOS 11 Big Sur as an installed OS and therefore cannot run it. It also cannot create a bootable usb stick with that OS.

If you cannot coax the 2014 mini to install Big Sur from internet recovery, then your next best option is to find another Mac that is capable of running Big Sur and try using that to create a bootable USB installer for the 2014. That would include iMacs and minis released between mid-2014 thru 2021 including the M1 Apple Silicon model. Also would be a Mac mini released between 2014 thru 2020, including the M1 models.

Create a bootable installer for macOS - Apple Support

As for the 2014 mini's inability to complete a Big Sur installation using internet recovery: if you are connecting that to the internet via wi-fi, then you might try using an ethernet cable directly to your router for a more stable connection.

Mindzman wrote:

I installed a larger HDD in my 2014 Mac mini.

The installer gets to "less than one minute" which we all know is Never True, but this has chocked for over 3 hours once and 2 hours a second time.

I would like to download an iso to make a bootable installer USB that has the complete system.

I find the os in the App Store and all I get is "this update is not available for this computer."

Mojave and later need APFS as a boot volume. APFS on a HDD (if by HDD you really mean HDD instead of SSD) does work as a boot disk but it is VERY slow. But 3 hours for the basic install to a freshly formatted HDD still feels excessive.

So use Internet Recovery and install from that whatever that gives. But then prepare and revert to High Sierra and MacOS Extended if you are really using a HDD as a boot volume.