US constitutional law does not refer to "natural rights", it refers to "fundamental rights". This enters into the doctrine of strict scrutiny vs. lesser scrutinies. If the US Constitution specifically names it, it is a fundamental right: bearing arms, speaking and worshiping freely, protections against search and seizure and so on. The Supreme Court can also recognize a right as being fundamental, even if it is not directly protected in the Constitution; for example there is no explicit provision protecting the right to self defense, interstate travel, marriage, privacy and freedom of contract, but these are or have been treated as fundamental rights.
Sometimes a fundamental right can be downgraded, such as the right to freedom of contract. In Lochner v. New York, 198 U.S. 45, the right to contract is taken to be a case of the right to liberty.
The general right to make a contract in relation to his business is
part of the liberty protected by the Fourteenth Amendment, and this
includes the right to purchase and sell labor, except as controlled by
the State in the legitimate exercise of its police power. Liberty of
contract relating to labor includes both parties to it; the one has as
much right to purchase as the other to sell labor.
But later, in Chicago, B. & Q. R. Co. v. McGuire, 219 U. S. 549, the court backpedaled a bit and said that
it was recognized in the cases cited, as in many others, that freedom
of contract is a qualified, and not an absolute, right. There is no
absolute freedom to do as one wills or to contract as one chooses. The
guaranty of liberty does not withdraw from legislative supervision
that wide department of activity which consists of the making of
contracts, or deny to government the power to provide restrictive
safeguards. Liberty implies the absence of arbitrary restraint, not
immunity from reasonable regulations and prohibitions imposed in the
interests of the community
and West Coast Hotel Co. v. Parrish, 300 U.S. 379 relied on this to essentially overturn Lochner (without expressly saying so). Parrish agred to work for less than state minimum wage, then sued for the difference. This court dismissed the supposed fundamental right to contract saying:
In each case the violation alleged by those attacking minimum wage
regulation for women is deprivation of freedom of contract. What is
this freedom? The Constitution does not speak of freedom of contract.
It speaks of liberty and prohibits the deprivation of liberty without
due process of law. In prohibiting that deprivation, the Constitution
does not recognize an absolute and uncontrollable liberty.
Sometimes, a fundamental right is explicitly recognized and relied on in a court ruling, such as the right to privacy in Union Pacific v. Botsford, 141 U.S. 250, where the court said that
No right is held more sacred, or is more carefully guarded, by the
common law, than the right of every individual to the possession and
control of his own person, free from all restraint or interference of
others, unless by clear and unquestionable authority of law. As well
said by Judge Cooley; "The right to one's person may be said to be a
right of complete immunity: to be let alone."
Note that the ruling does not call it a "fundamental right", but the notion of fundamentality is clearly there in the ruling. Other examples are the right to marry (Loving v. Virginia, 388 U.S. 1):
The freedom to marry has long been recognized as one of the vital
personal rights essential to the orderly pursuit of happiness by free
men. Marriage is one of the "basic civil rights of man," fundamental
to our very existence and survival.
Also, the right to chose to use contraceptives is a fundamental right (Eisenstadt v. Baird, 405 U.S. 438 – note how this depends on and elaborates the right to privacy)
If the right of privacy means anything, it is the right of the
individual, married or single, to be free from unwarranted
governmental intrusion into matters so fundamentally affecting a
person as the decision whether to bear or beget a child.
Roe v. Wade also relies on the right to privacy. The court notes that "The Constitution does not explicitly mention any right of privacy", and then lays out how it is implicit in the Constitution.
There is a vast area of actions that might reasonably be taken to be fundamental rights, but have not been ruled on one way or the other. If (in some bizarre dystopian future scenario) a law were passed that made it a crime to grow and use plants, it would not be surprising if SCOTUS ruled that such a law violates a fundamental right, but it almost certainly would be something much more general than "growing plants".
Wickard v. Filburn, 317 U.S. 111 already spells trouble for a supposed fundamental right to grow plants. In this case, appellee grew wheat, but the growing of wheat (and a few other crops) were subject to federal regulation. The court ruled that
The effect of the Act is to restrict the amount of wheat which may be
produced for market and the extent as well to which one may forestall
resort to the market by producing for his own needs.
The Commerce Clause of the Constitution authorizes Congress to limit interstate commerce. Even though Filburn was not selling the wheat to another state, he also was not buying it from another state, and he was thus (minutely) affecting interstate commerce:
that the production of wheat for consumption on the farm may be trivial in
the particular case is not enough to remove the grower from the scope
of federal regulation where his contribution, taken with that of many
others similarly situated, is far from trivial.
Another indication that there is no absolute fundamental right to grow plants is
Gonzales v. Raich, 545 U.S. 1, which held (relying on Wickard) that "Congress' Commerce Clause authority includes the power to prohibit the local cultivation and use of marijuana in compliance with California law".