It’d be a fair bit of work, but from a technical point of view you could implement a click and a drag event handler that “selects” the text, and intercept Ctrl+C etc and place the text on the browser clipboard.

Ultimately it would probably feel quite unnatural compared to the native text selection of the browser. And probably would not work very well except in a small subset of browsers.

I think at some point in the future browsers and/or operating systems will ship with machine learning powered systems for recognizing text in bitmaps and for letting users copy recognized text. This is already possible today both with third party non-ML powered OCR software and with third party ML-powered software.