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You can't, and it sucks. That's why the web is better, or at least why it's supposed to be better.

Taking screenshots and zooming in on those... a very tedious process.

With iOS you don't need to do this. You can enable zooming as a system-wide feature. You can even zoom parts of the screen, like a magnifying glass. You can find all of these settings under Settings -> Accessibility -> Zoom.

android has the same thing. you can activate an accessibility setting and then a triple tap will zoom in everything system-wide

Unfortunately the UX of that feature isn't great, so it's only useful in some cases. Often I find the screenshot method easier/faster.

You can change the OS text size and apps will respond to it.