You might have gotten it wrong. Sabine says you can modify the state on one particle without modifying the state of the second particle. In the video ChatGPT says the opposite, affecting a single particle in the entangled pair affects the whole pair.
Both might be right in a sense, as both are speaking loosely. Let's write a Bell state for two particles A and B (or EPR pair as you call it):
$$|\psi\rangle=\frac{1}{\sqrt{2}}(|+1,-1\rangle+|-1,+1\rangle)$$
where I am using Sabine's notation. This state is a superposition between measuring particle A to be aligned with your measuring device (+1) and B to be anti-aligned (-1), and the state where A is anti-aligned and B is aligned. There is a 50% chance of measuring either.
There is always an operator $X$ such that acting on a single particle does the following $X|+1\rangle=|-1\rangle$ and $X|-1\rangle=|+1\rangle$. How do you create this operator physically? There are many ways, and example would be a magnetic field in a certain direction that makes the spin precess (note that this does not represent a measurement). In the language of spins it is the $\hat S_x$ operator or in the language of qubits it is the Pauli matrix X.
What happens if we apply $X$ only to the first particle (A) of $|\psi\rangle$?
$$X_A|\psi\rangle=\frac{1}{\sqrt{2}}(X_A|+1,-1\rangle+X_A|-1,+1\rangle)=\frac{1}{\sqrt{2}}(|-1,-1\rangle+|+1,+1\rangle)$$
Here you only acted on a single particle and still you have an entangled state: 50% of both being +1 or 50% -1. By flipping one of the spin, you perturb the system in the sense that you no longer have the same global state and thus different results. In another sense, you only acted on a particle you did not affect the state of the other (which was undefined previous to measurement anyway).
