Why are those objectively useful metrics for productivity though? I can think of a dozen reasons why they aren't, as opposed to why they might be. Which, I guess, makes their objective usefulness subjective.
Some people will be working on longer lived feature branches because they're more complex, so they end up with one merge to master in the time it took the dev updating REST APIs to accommodate a new optional parameter to merge four branches.
Someone writes four tests that another dev might cover in one because the four assertions were all closely related to the same invariants and code paths. Who was actually more productive?
One developer pushes to production three times in one day because they typoed a property name twice... ...etc. etc. ad nauseum.
If you seriously believe that these metrics are objective methods of measuring developer productivity, I strongly suggest you spin off a business, because you're about to make millions.