You can't, and it sucks. That's why the web is better, or at least why it's supposed to be better.
You can change the OS text size and apps will respond to it.
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.