Hi, welcome to the Typst forum! I’ve adapted a bit your question title to match our guidelines.
I think your problem is actually unrelated to the font: by default the integral sign is not scaled. It’s just that the default font (New Computer Modern Math) has a larger symbol than TeX Gyre Pagella Math.
You can scale the symbol manually if you want:
#show math.equation: set text(font: "TeX Gyre Pagella Math")
$
stretch(integral, size: #3em) ((sqrt(f) + 1/2 g t sqrt(f) + epsilon(t))^4 - sqrt(f)^4)/t
$
