Cannot free disk space on 2017 MacBook Air. can I delete contents of com.apple.iconservices.store?

I am having trouble clearing disk space on a 2017 MB Air with a 121GB SSD running Catalina 10.15.6

The disk has about 800MB available space according to all tools that have scanned it. But it should have nearly 80GB free. The user was deleting all of his clutter trying to clear space, but the available storage never changed. Each volume shows its correct content plus very little free space and the bulk of their capacities is allocated to "Other Volumes"

I have tried everything in every thread that I can find, including stack exchange and Apple communities. I could list out everything I have tried, but it is quite the list. Ill give an overview and I can provide more details as required.

I have tried all of the solutions involving removing Time machine local snapshots, including all of the diskutil commands found on this stack exchange thread, which was the most extensive thread I found.

https://apple.stackexchange.com/questions/44203/disk-space-not-freed-up-after-deleting-files-and-emptying-trash

The only thing on that thread I cannot do is reinstall the OS because there isn't enough disk space. I also cannot create a Time Machine backup, because there is not sufficient disk space to create a local snap.

I also noticed there is an extra volume that I do not see on other Macs in the company. Its called "MacintoshHD Data". I am considering deleting it and seeing what happens, (already backed up the files manually) but I would much rather understand what's going on here, since we have another MB Air running Mojave which is starting to exhibit similar problems. I noticed (working as root user in the GUI) that the folder "com.apple.iconservices.store" shows a total size on disk of 135.8MB but when I start adding up its contents manually I get something more like 942MB+. Probably not the issue but I am running out of ideas!

Someone already asked about deleting the contents of com.apple.iconservices.store on another thread but the answer they got was "You should not be able to see that folder, its protected", or words to that effect. Somehow, that was considered an adequate response and the thread was closed. That doesn't actually answer the question as stated though.

Ultimately what I need is a solution to the Other Volumes disk space problem. One that doesn't involve TimeMachine Snaps, because there are none in the SSD from what I can tell.