How to examine and reduce what “About This Mac” categorizes as “System” disk use

Other is a catch-all by taking the drive's max capacity and subtracting the sum of all other counted file sizes. So, if your drive has corruption where many blocks are unavailable or lost, you will see large other "allocations".

If the other space remains the same after running disk utility to verify and/or repair the volume then you can assume it's really files taking that space.

The categorization comes from spotlight indexing, so you could search here how to rebuild that index if you suspect bad metadata leading to an incorrect storage report.

The simplest way to rebuild the metadata (spotlight) index is to simply add your hard drive to the spotlight privacy list in system preferences and subsequently remove it. The built-in help should have a guide if you're not sure how to refresh all spotlight data.

There certainly isn't the same amount necessary as the DMG, so you sure can mount a 100GB DMG into a file system that has less (there will be trivial consumptions, maybe a few kb, but nothting that you'll notice).

The whole thing works in the way, that the system attaches a file-system driver to the file with the DMG. The driver will present the DMG file to the system like an "external" drive and perform file requests on behalf of the system on the contents of the file.

Essentially the driver will says to MacOS: We have a new volume here. So MacOS will then ask the driver. "Give me a list of content in it", and then the driver examines the inside of the file and presents the list of files organized inside the DMG. Etc.