Interesting. I screenshot then send to Google Lens which is obviously more of a hassle than what you're describing. But I have gestures enabled and so no home button. I wonder what is the gesture-equivalent of long-pressing on home.
On my Pixel 5, if you swipe from the bottom bar up (as if you are gesturing to close the app), near the bottom some options will appear: Screenshot or Select. The Select mode is an OCR enabled text selection.
This just takes me to the horizontal scrolling list of apps displayed as screenshots of the app.
I can swipe from the bottom corner to bring up "Gemini" but that doesn't have an option to OCR the screen. Android is so diverse - people always end up talking about their unique and differing experiences, unfortunately.