Why is $\pi$ in the domain of filters?
In discrete time, distinct frequencies only have sense in a range of $2\pi$ (where the units are radians per sample).

A sinusoid (or complex exponential) of frequency $2\pi$ is indistinguishable from one with frequency 0. If in doubt, evaluate $x[n] = \cos(2\pi \times n)$ and $x[n] = \cos(0 \times n)$. Same thing with any two frequencies separated $2\pi$ or multiples of $2\pi$.

For example, you can easily show that $\cos( \theta_0 \times n ) = \cos((\theta_0 + 2k\pi) \times n)$ for any integer $k$.

So a range of size $2\pi$ is enough not to repeat frequencies.

In general, the range chosen is $-\pi \cdots \pi$, where $\pi$ is the maximum frequency ( $\cos(\pi \times n ) = (-1)^n$ ).

In the $z$ domain, the frequency response is the transfer function ($H(z)$) evaluated on the unit circle ($z = e^{j\theta}$), so here again you have the range $2\pi$ before repeating your path.