I think [site:mysite.com] is the search operator I use the most.
It helps me in seeing the big picture of the site’s content, such as how often the site is publishing a new content item, which type of content, URL structure and more.
It can also assist in identifying the content gap in numbers between different sites.
Lately I noticed that using the search operator [site:] on Google, returns only the pages that are indexed, without any reference to the total number of these indexed pages🔢
Ok. We all know that for your site, you may go to Search Console to get this question answered.
But what about when you want to understand how many pages of your competitor’s site are indexed on Google?
In the past (like a week or so ago) you could just type [site:mycompetitorsite] and you got the answer, but now Google is somehow hiding this info so you need to click on the “tools” and then you’ll get the answer on the right:

In any case there are also chrome addons you can use to see this number:
💡 Add a chrome addon such as “Search Enhancer for Google“
💡Type site:mycompetitor.com
💡Scroll down to the end of Google’s results page and check the number of pages it shows

If you multiply it by ~10 (the average number of results per page) you’ll get a very good estimation of your competitor’s number of indexed pages on Google
It’s not faster as site:mycompetitor.com used to be, yet it does the job
Not sure how to get other info you’re missing?
Let’s chat