Sovereignty was vested in the Crown through the assertion of sovereignty by the Crown in 1840, followed by the erection of New Zealand as a separate colony in its own right. In early 1841 the new colonial government was in place and the constitution of New Zealand was established. As part of a Crown colony the constitution was that of the British Crown with the Queen as the head of state with laws made by the British parliament or the New Zealand Executive Council.
General property rights in Article 2 were established for all new Zealanders through colonial laws and the exercise of sovereignty.
However, the guarantee to protect the existing property rights (at 1840) of all New Zealanders has never been incorporated into New Zealand law. So they are not enforceable in New Zealand courts and they cannot be part of the constitution of New Zealand. (The Waitangi Tribunal was formed in 1975 as a commission of inquiry to make recommendations to the government on breaches of "the principles of the Treaty", not on breaches of the articles of the Treaty.)
The New Zealand Constitution Act 1852 was an Act of the Parliament of the United Kingdom that granted self-government to the Colony of New Zealand. This was superseded by the Constitution Act 1986.
Constitution Act 1986 https://www.legislation.govt.nz/act/public/1986/0114/latest/DLM94204.html#DLM94233The Constitution Act 1986 is an Act of the New Zealand Parliament that forms the backbone of the New Zealand’s constitution. It lays down a framework defining fundamental political principles of governance, and establishes the powers of the executive, legislative and judicial branches of state. It outlines the roles and duties of the monarch, the governor-general, ministers and judges.
According to the Notes to the Act it is “An Act to reform the constitutional law of New Zealand, to bring together into one enactment certain provisions of constitutional significance”.
The key provisions are:
2 (1) The Sovereign in right of New Zealand is the head of State of New Zealand, and shall be known by the royal style and titles proclaimed from time to time.
2 (2) The Governor-General appointed by the Sovereign is the Sovereign's representative in New Zealand.
3A (1) The Sovereign or the Governor-General may perform a function or duty, or exercise a power, on the advice and with the consent of the Executive Council ...
11 (1) A member of Parliament shall not be permitted to sit or vote in the House of representatives until that member has taken the Oath of Allegiance in the form prescribed in section 17 of the Oaths and Declarations Act 1957.
(2) The oath to be taken under this section shall be administered by the Governor-General or a person authorised by the Governor-General to administer that oath.
14 (1) There shall be a Parliament of New Zealand, which shall consist of the Sovereign in right of New Zealand and the House of Representatives.
15 (1) The Parliament of New Zealand continues to have full power to make laws.
16 A Bill passed by the House of Representatives shall become law when the Sovereign or the Governor-General assents to it and signs it in token of such assent.
Allegiance to the Crown is guaranteed through oaths of allegiance. Members of Parliament swear the Oath of Allegiance (s 11 (1)) under section 17 of the Oath and Declarations Act 1957 in the following form:
I, [specify], swear that I will be faithful and bear true allegiance to His Majesty King Charles the Third, His heirs and successors, according to law. So help me God.
https://www.legislation.govt.nz/act/public/1957/0088/latest/DLM316132.html
New Zealand judges are also required to swear the judicial oath under section 18 of the same Act:
I,..., swear that I will well and truly serve His Majesty King Charles the Third His heirs and successors, according to law, in the office of .........; and I will do right to all manner of people after the laws and usages of New Zealand without fear or favour, affection or ill will. So help me God.
Oaths are also sworn by members of the Executive Council, the Governor-General, Parliamentary Under-Secretaries, the Armed forces and the Police. Those becoming New Zealand citizens are obliged to swear an oath of allegiance to the reigning sovereign.
This all goes to illustrate that in 2023 the constitution of New Zealand is based on the absolute sovereignty King Charles the Third as the Sovereign in right of New Zealand.
Note that there is no mention of the Treaty or its articles in the Constitution Act 1986. Likewise there is no mention of the principles of the Treaty.
https://thetreatyfacts.blogspot.com/p/6-treatys-significance-today.html