You can do something like this via the browser by printing the page to PDF then using Inkscape to convert that to SVG. I documented this here: https://www.checkbot.io/article/web-page-screenshots-with-sv.... There's a few caveats though like box-shadows getting converted into bitmaps and vectors not being grouped in layers like you'd expect, plus it's heavyweight if you're wanting to script it.
I'm curious if Satori could be used to capture in-app client-side screenshots accurately.
There was some Google properties that had some in-page tool to screenshot the page - wonder how they did that one?
It's all client-side apparently, essentially by writing a page renderer in JavaScript. See:
https://stackoverflow.com/questions/4912092/using-html5-canv...