DOC: build shouldn't succeed if an error is raised in a notebook or script

[neutrinoceros]

Bug report

Bug summary

As recently shown by #3500 (and I believe on several occasions before that), our infrastructure currently allows for "passing" documentation builds even when errors are raised in notebooks.
There should be a way to fix this so we can't solve issues when they are introduced instead of when they are manually reported.

In a sense, this is complementary to #3369, but probably more crucial.
Since #3369 is currently in the 4.1 milestone I'll put this one in too, in hopes that it can at least be discussed in a foreseeable future, though it should never be considered blocking, and could easily be postponed if necessary.