Whether the gun stays in the state or not is irrelevant to what you are asking. What you need to ask is the following:
Does my situation meet the definition for "residency" given the law and the interpretations of the ATF?
ATF states the following:
"A person’s “State of residence” is defined by regulation in 27 CFR 478.11 as “the State in which an individual resides. An individual resides in a State if he or she is present in a State with the intention of making a home in that State.” Ownership of a home or land within a given State is not sufficient, by itself, to establish a State of residence. However, ownership of a home or land within a particular State is not required to establish presence and intent to make a home in that State. Furthermore, temporary travel, such as short-term stays, vacations, or other transient acts in a State are not sufficient to establish a State of residence because the individual demonstrates no intention of making a home in that State."
Is your stay at your parents considered "short-term?'
Is your stay at your parents considered "transient".
You yourself state that you are staying there during COVID 19. Arguably, COVID 19 is not going to last forever. What are your plans after society gets the all clear?
Are you going back to NYC.
Your situation does not sound like you have the "intention of making a home" in the state.
However, this is a grey area, as there is no definition anywhere in the statute or otherwise where "short-term", or, "transient" are legally defined.