Here is the New York law: VAT section 250
2 . A person of the age of sixteen years and upwards who shall be
a nonresident of this state, and a resident of a state, territory,
federal district or foreign country having laws, with which
such person has complied, which require such person, in order to
operate a motor vehicle or motorcycle therein, to be licensed, may
operate or drive a motor vehicle or motorcycle on the public
highways of this state without being so licensed under this
chapter, [...]. A nonresident entitled to operate a motor
vehicle or motorcycle as herein provided who shall become a
resident of this state may operate or drive a motor vehicle or
motorcycle on the public highways of this state for a period
not exceeding thirty days from the date he becomes a resident
pending the obtaining of a license to operate such motor vehicle
or motorcycle in this state.
5 . As used in this section, the term "resident" shall
mean domiciliary, that is, one who lives in this state with the
intention of making it a fixed and permanent abode. It shall be
presumptive evidence that a person who maintains a place of abode
in this state for a period of at least ninety days is a resident of
this state.
So just because you are "living" in New York does not mean you cannot drive on your out-of-state or foreign license, as long as you do not have the intention of making New York "a fixed and permanent abode".
Here is the Washington state law: RCW 46.20.025
The following persons may operate a motor vehicle on a Washington
highway without a valid Washington driver's license:
(2) A nonresident driver who is at least:
(a) Sixteen years of age and has immediate possession of a valid
driver's license issued to the driver by his or her home state; or
(b) Fifteen years of age with:
(i) A valid instruction permit issued to the driver by his or her home
state; and
(ii) A licensed driver who has had at least five years of driving
experience occupying a seat beside the driver; or
(c) Sixteen years of age and has immediate possession of a valid
driver's license issued to the driver by his or her home country. A
nonresident driver may operate a motor vehicle in this state under
this subsection (2)(c) for up to one year;
It doesn't define "home state" or "home country", but since it is in the context of "nonresidents", it probably refers to the state or country you are a "resident" of. Washington state defines "resident" for the purposes of getting a Washington state driver's license in RCW 46.20.021 as
(3) For the purposes of obtaining a valid driver's license, a resident is a person who manifests an intent to live or be located in this state on more than a temporary or transient basis.
Assuming that it considers the residence the same way for nonresidents as for its own driver's license, this means that the home state/country would be the one where you have an "intent to live on more than a temporary or transient basis". If you do not have such an intent in New York and have such an intent in Germany, then I would argue that you can drive with your German driver's license in Washington state (as well as New York state).