Google and all modern search engines all frame the objective of search as finding relevant "pages". I think there's a big opportunity to create another search index with results being domains. Where I can search by keywords of site content. But I can also search at the meta level; single/multi author, page count, page length, monetized, comments section.
I think this is somewhat analogous to the Small Web project. With the ability to search using metadata criteria, I could essentially find domains that satisfy my own Small Web criteria.
For example, when doing research on a more niche topics -- where exploration is more open ended -- I've found it more effective to find a site that specialized in a topic or community and reading through a site's back catalogue. While reading I'm building up terminology, links and context which make standard page searching much more effective.
Another good use case is curating my RSS feeds. I'm always hunting for a good blog to follow. I'll often go through and rotate feeds out which keeps it interesting and avoid making an echo chamber.
As Lens
The least invasive implementation would be to reuse the Lens system. I think a domain result can almost entirely reuse the page result layout using the index/home page as proxy for the domain as a whole. The unqualified search terms would search site keywords and content. Searching site metadata would fit best in the advanced search options; mostly because they would be relevant in page based search too. While custom operators would be cool I think it would be an ontology trap trying to come up with good operators.
As Listicle style result group
If it were possible to domain search within the context of normal page search, the results could be grouped in the same way that listicle results are grouped together under a header. This probably is harder because it would require a semantic analysis of the search terms to determine the user is looking for sites rather than pages.
Two layer auto completion
Another workflow I would find useful would be analogous to the fuzzy file and fuzzy content search UX that you get in text editors like neovim's telescope. For those not familiar, this is searching by file or directory to select candidates, then searching the file contents. Applied to web search you would search by domain where the selected domain(s) could be used as one or more site:example.com
filters added to your next query.
Some recent examples from my random train of thought:
Blog search
- Query: "eurasian archeology blogs"
- Advanced options: Less than 1,000 pages, new post within the last 2 years.
Niche community
- Query: woodworking "hand tools" "block plane" restoration identification -site:reddit.com
- Advanced options: type wiki or forum