Wikipedia's article titled "Equal footing" states that
The equal footing doctrine, also known as equality of the states, is the principle in United States constitutional law that all states admitted to the Union under the Constitution since 1789 enter on equal footing with the 13 states already in the Union at that time.
However, this doctrine is not in the Constitution, but apparently was adopted by Congress each time a new state was admitted. However, the article asserts that
the Supreme Court asserted, in Lessee of Pollard v. Hagan (1845), that the Constitution mandated admission of new states on the basis of equality".
. . . and then the article mentions two later Supreme Court rulings saying this is a Constitutional principle.
However, this has been asserted to apply only to states that have been admitted to the Union, not to state within the territory of the U.S.A. that have not been admitted to the Union but are nonetheless states. Here it may be asserted that no such states can exist, or at least that none have existed.
However, look at the Northwest ordinance of 1787 and its amendment in 1789. The 1787 ordinance was enacted by Congress while the Articles of Confederation were still in effect, and it said
There shall be formed in the said territory, not less than three, nor more than five States; [ . . . ] And whenever any of the said States shall have sixty thousand free inhabitants therein, such State shall be admitted, by its delegates, into the Congress of the United States, on an equal footing with the original States, in all respects whatever;
(Ultimately that territory became five states and part of a sixth.)
This seems to say that before the population of one of the proposed states reached 60,000, they would not yet be admitted on an equal footing, but would nonetheless be states. The equal-footing doctrine applies only to states admitted to the Union, and not to any of these proposed not-yet-admitted states, but that they would still be in some substantial sense states. As states, presumably they would have constitutions enacted by the voters of the state and otherwise not be under federal jurisdiction in the way in which organized incorporated territories are.
In 1789, after the present Constitution was in effect, Congress altered the ordinance for the purpose of adapting it the the new Constitution, but the only adaptation was that reports that the territorial governor had been required to submit to Congress were to be submitted instead to the President.
So here we have an act of Congress under the present Constitution saying states could exist within the boundaries of the U.S. that would not yet be admitted states, thus although they were states, the equal-footing doctrine would not apply to them.
No such states were ever created under the authority of Congress. However, there was one occasion when Congress allowed that a certain entity within the boundaries of the U.S. was already a state but not yet an admitted state, and decided that it would get admitted. That was Vermont. When Vermont was admitted to the Union in 1791, the 1786 "Constitution of the State of Vermont" continued in effect and the man who had begun a one-year term of office as "governor of the state of Vermont" in October 1790, succeeding the previous "governor of the state of Vermont", continued his one-year term of office uninterrupted, as did all other officers of the state. When he assumed office, Vermont had not yet assembled its convention that met in January 1791 to decide whether to apply for admission to the Union. Under Vermont law, no new State of Vermont was created at that time, but rather the same state continued to exist, and Congress said that the entity that had petitioned them for admission was "the State of Vermont", and they were granting the petition.
One can argue that Vermont cannot serve as a precedent because it was organized before even the Articles of Confederation were in effect and before the boundaries of the U.S. were defined (that first happened in the Preliminary Articles of Peace of 1782 and wasn't really in effect until the peace treaty of 1783 was effective) -- it was entirely unique. No other state can ever be in that situation. And throughout the 1780s, the state of Vermont took the position that Vermont was not within the U.S., even though the peace treaty, to which Vermont was not a party, said it was.
But there is the Northwest Ordinance, authorizing the creation of states that would be states but would be not-yet-admitted states, to which equal footing would not apply.
If one takes the equal-footing doctrine to be a part of the Constitution although nowhere explicitly stated in the document, could one say that (1) it applies to admitted states but (2) not to non-admitted states, but (3) those could exist within the boundaries of the U.S. and still be states? Or, alternatively, is that provision of the Northwest Ordinance unconstitutional?