I noticed that the automatic adjustment size for parentheses by use of \left(...\right) "fails" in two cases I use a lot:
Case one:
When a upper index is set as \text{...}. I typeset label-indices as \text{...} (for example $y^\text{p}$ for predicted y-values) since this is how they are usually formatted in the physics context to distinguish labels from mathematical indices.
I marked the upper and lower ends of the parentheses for just brackets (green), \left(...\right) (red) and \left(...^\text{...}\right) (blue). Note that the bracket size for the latter is adjusted, but not to the right size.

Case two:
When having large equations in parentheses spanning multiple lines, I break the lines with
\begin{align}
\left[ ... \right. \\
\left. ... \right]
\end{align}
In this case, the size of the square brackets is not adjusted synchronously. I understand that this is because the size is determined within a line instead of within the \left[...\right] pair.
Question:
The question connecting this two cases is: Is it possible to access the logic of how the sizes are determined? (Another use case is to increase nested brackets automatically).
Example:
MWE:
\documentclass[preview]{standalone}
\usepackage{amsmath}
\usepackage{listings}
\lstset{language=TeX,
basicstyle=\footnotesize\ttfamily,
}
\begin{document}
Case one:
\begin{align}
(y_i^f) + \left(y_i^f\right) + \left(y_i^\text{f}\right)
\end{align}
Case two:
\begin{align}
y=& \left[ \frac{x}{c} \right. \
&+\left. f(x)\right]
\end{align}
\end{document}



\text{f}is wrong markup (and slow) it will pick up whatever font is current outside the math, better to use^{\mathrm{f}}– David Carlisle Dec 21 '20 at 15:52\bigl... \bigr,\Bigr ... \Bigrand the like. – Bernard Dec 21 '20 at 15:53\bigl(and\bigr), I'll find a link to the standard answer. – David Carlisle Dec 21 '20 at 15:54\texttry placing this in a theorem using italic text for example. – David Carlisle Dec 21 '20 at 16:07