Have a look at very similar question at https://learn.microsoft.com/en-us/answers/questions/1136333/datestamps-in-excel-when-a-cell-value-changes the formula there works for showing dates of cell changes, you will need to add a comparison cell and iterative formulas to make it work. it's all explained in the solution,
P.S the formula you give above activates on the else part of if statement and will i believe update on every call of the today function and not only when the entry is changed in the referenced cell