Having used the verbatim option on and off since creating this topic, I have a few notes.
It's the behaviour I always want from a search engine. Match all of my terms across results.
However, verbatim, is too ... verbatim.
I make typos, and I want search engines to account for that, like the non verbatim option does. In all honesty, the only time I'd like true verbatim "character by character" match is when I paste an error message in my search, and that error message includes typos. Which could just as well be enabled by quotes around my query "phase search", instead of a configurable option (which also used to be how I'd query those in Google before it started getting too liberal with my search terms).
In summary I think that results should include all search terms in non verbatim mode.
And when it comes to signaling within the UI, alongside the "show more results" button, there could be an "switch to a less strict search for your query" / "try a more exploratory search" or something along those lines that switches on the (now) current search behaviour.