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Yeah, that shit has been driving me crazy for a long time now. I imagine a batty old librarian riffling through a filing cabinet of my emails saying "ooh wait, I found more!"

It's an estimate. It would add additional time to the search to calculate an exact number.

If it works like Google-Search, results are not an estimate, or not even random, it looks like it is inflated .... for example, if you navigate to https://www.google.com/search?q=zzzfgh , it tells you 5,900 results until you reach a page where there is no more results and it tells you 484 results (for example, I never seen an estimate that was lower then the real count)

Duplicate removal generally happens after the initial count is received. That's why you can get major variations in the count and the actual number of results.

If I click: "If you like, you can repeat the search with the omitted results included.", I still don't get anywhere close to the initial count.

A very poor estimate.

You know, I still wonder the same thing, "1-20 of many" is quite annoying too..

Because they estimate to save resources?