NY Est Pow & Trusts L § 3-2.1(a)(1)(C)(4) requires that
There shall be at least two attesting witnesses, who shall, within one
thirty day period, both attest the testator's signature, as affixed or
acknowledged in their presence, and at the request of the testator,
sign their names and affix their residence addresses at the end of
the will. There shall be a rebuttable presumption that the
thirty day requirement of the preceding sentence has been
fulfilled. The failure of a witness to affix his address shall not
affect the validity of the will.
That means that the witnesses attest to having seen you sign the will, and you must know that it is a will being signed. There is no requirement that they see the will itself, and they do not "attest" anything regarding sound mind, memory or testamentary capacity. It is not required that witnesses receive a copy of the will (for any reason), and it is probably extremely rare for them to do so.
However, a witness could be called, during a subsequent court procedure, to testify as to relevant facts such as that a beneficiary held a gun to the testator's head.