P=Q

If $p = q$ then $N = pq = p^2$ and you can use function such as isqrt in Python to retrieve $p$.

Note that in the situation $N=p^2$, $\phi(N) \neq (p-1)^2$ due to the full definition of Euler's totient function:

$$\phi(n) = n \prod_{p|n} (1-\frac{1}{p})$$

The key here is that $p \mid n$ are distinct prime factors, so we would only use $p$ once in the equation:

$$\phi(n) = n(1-\frac{1}{p}) = n - p$$