When a variable $y$ depends on other variables, say $y=c x^3$, one often writes $$y|_{x=2}$$ to say "$y$ when $x$ has value $2$". This might be more familiar in the context of derivatives where we find $\left. \frac{dy}{dx}\right|_{x=2}=12c$. It also appears in other areas of mathematics. For example the fiber of a bundle $E$ over some point $p$ is often denoted with $E|_p$. If we interpret a fiber bundle as a space depending on points of the base this seems to be analogous to the previous example.
Notice that in the example $y=cx^3$ it would be wrong to write $y(2)=8c$ since $y$ is not a map of type $\mathbb{R} \to \mathbb{R}$.
Question 1: Who introduced this bar notation?
Question 2: How did people in the early days express "$y$ under the condition that $x=2$"? I'm guessing they just used words, but was there an alternative notation? Or did they abuse the notation for function application, as in $y(2)$, once Euler/Bernoulli had introduced it?