There is this Post here on a tool for Firefox which is 8 years old.
I am using a browser version of a Validator on Chrome which only does HTML and only does one page.
I am looking for something that could do the whole web site, either by using the sitemap or another file where I can list the pages. It can do it on my PC with Xampp or on the live version of my website. I don't mind paying up to about $100.