In z-transform, if z means "delay", why do we talk about the value of z?
It is a bit to wrap your head around.

Mathematically, if you denote the z transform as $X(z) = \mathcal{Z}\left \lbrace x_k\right \rbrace$, then when you take the transform of $x_k$ after it's been delayed by one sample you get $\mathcal{Z}\left \lbrace x_{k-1}\right \rbrace = z^{-1}X(z)$.  Except in strange corner cases* this always works, and you don't need to know $X(z)$ to know it works.

So $z^{-1}$ (and thus $z$) are frequency-domain variables, just like the $k$ that gets lost in the transform from $x_k$ to $X(z)$ is a time-domain variable.  But $z^{-1}$ acts exactly like a delay operator, so in most circumstances you can treat it as such.

* Which I can't even call out -- you simply don't run into them in practice.