It indexes pages which were already visited, right?

Yes, if you use the browser extension only, but Hister has an API and a crawler as well if you’d like to add content you have not visited yet. Also, Hister supports indexing local text files, not just websites.

Afterwards, that website is in my browsing history and if I need it again, I don’t need to search for it

• Unfortunately browser history does not include the page’s content only the URL + title combo at best.
• Browser’s can’t show an offline preview (Having offline previews is a huge privacy - and productivity - win in my opinion, it completely eliminates the need of creating external network requests)

These are the biggest weaknesses of the browser history compared to Hister, but there are many more nuances where Hister can provide extra features and QoL improvements. I recommend checking the documentation & posts on the website if you are interested in the details.

Also how I would imagine it is default search there and if no hit then fallback to a default search engine, e.g. DDG.

This is exactly how I use it. Hister has even a hotkey to quickly jump to your preferred online search engine with the current search query if you cannot find what you are looking for.