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I've never heard of a warrant for any product to add an additional original warranty period after a warranty replacement was used. You would just get whatever amount of warranty was left.
It is common for an automotive part to come with its own warranty. For example, a Tesla drive unit installed in a RAV4 EV one month before the Powertrain Warranty expired comes with a 1 year warranty. If it fails 10 months later, 9 months after the powertrain warranty expired, it’s still covered. Maybe a different business entity is paying, but it’s covered at no cost to the vehicle owner.