Hi @Max C.C
In my 2 test envirionments, one with Microsoft 365 Apps installed and the another with Office 2010 install, but I can not reproduce the results as your sharing file, as deleting cells via "Shift cells left" or "Delete entire column", theses actions will not be tracked as changes.
If you select the column > Delete Cells > Shift cells up, the content will be deleted and tracked but the column is not deleted.
Besides, I searched online, there is an article "Deleting Table Columns with Track Changes Turned On", which also said: There is no way to force Word to delete the column and track the change. This appears to be because deleting a column is too complex of an edit for Word to track. All you can do is come up with ways to work around the limitation.
If I find any updates, I will post back.
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