How to search the fully rendered view in Safari?

Yes. You can use the KM Execute a JavaScript in Front Browser action.

This JavaScript will return all rendered text currently showing on the page:

document.body.innerText;

You could then search that text as you like.

However, you might also be able to search/compare the exact field/text of interest, using a querySelector() statement. If you'd like help with that, please post the page URL (or HTML code in a Code Block) and screenshot of the target region with the target data clearly identified.