Automatic brackets size with left(...right) fails for text{...} exponents

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=footnotesizettfamily,
}
begin{document}

Case one:
begin{align*}
    (y_i^f) + left(y_i^fright) + 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} 

documentclass{article}

usepackage{amsmath}

begin{document}

[
left(y^f_iright) left(y^{text{f}}_iright) left(y^{mathrm{f}}_iright) 
]
end{document}

[
(y^{mathrm{f}}_i)left(y^{mathrm{f}}_iright) 
]