To install a macOS upgrade, you should have at least 50GB of Free storage space. Ignore the "Available" space designation since some of that space is not immediately accessible, but will be released for use at some unknown time in the future. It is unfortunate the "Available" value is what Apple lists in most places, but it is a misleading value. You can compute the actual Free space by using the following formula:
Free space = Available space - Purgeable space
The "Purgeable" space value is typically in parentheses after the "Available" value. Or you can view the Free space value which is listed within Disk Utility (select the "Data" volume on the left pane of Disk Utility, and you will see the "Free" space value listed on the right pane just beneath the storage graph).
There is no way to reduce the storage designated by "System" because that is being used by macOS for one reason or another. Some of the "System" storage may be released at some point, but that will be up to macOS itself. About the only thing you may possibly be able to do is make sure all of your backups have completely transferred to external media so that the backup APFS snapshots are deleted (may be a day or two, but sometimes a snapshot may be kept longer....check the backup app's settings). APFS snapshots can contain data you have already deleted. You can view & delete APFS snapshots by using the information in the following Apple article (if the backups have not been transferred, you may not have a needed version of a file in an emergency):
View APFS snapshots in Disk Utility on Mac - Apple Support
If you don't have any APFS snapshots to delete, then you will need to try to delete files located within your home user folder (or from other macOS user accounts if you have more than just your main user on this Mac).
FYI, you should always have at least 20GB of Free storage at all times for the normal operation of macOS. For some workloads, you may need to always keep even more Free storage at all times.
Unfortunately a 120GB SSD is extremely small and can only accommodate a small amount of user data. It is embarrassing that Apple kept offering them as an option for so long.
