Hey everyone, The point is that I have managed to find some spell checking software, but it processes each url separately or text copy-paste is required. I need to find proper one, which can check all website pages thoroughly once url is provided

A1 Website Analyzer can do this:
https://www.microsystools.com/products/website-analyzer/help/website-spell-checker/

(you may have to teach it about niche specific works, so the first time you run it there may be some words you need to add)

Use Grammarly!!

hey thnx for information

 Grammarly is the best  spell checker tool.