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Is it possible to automatically color cell backgrounds if their values has been changed (in my case, the only time a cell changes value is by manual user edit/input - no cell values are computed of functions of other cells)?
Yes, it's possible by using Google Apps Script. For further details please add a brief description of your search/research efforts as is suggested in How to Ask.
You could use the an edit trigger (simple or installable). The edit event object include value and oldValue properties but only when a single cell is edited, so if you are expecting data being added by copy/pasting multiple cells then you should make a copy of the values somewhere.
value
andoldValue
properties but only when a single cell is edited, so if you are expecting data being added by copy/pasting multiple cells then you should make a copy of the values somewhere.