I think that it might be useful to add somewhere advice about other possibilities how to search. (I am not sure what would be right place, but it would be nice to have it somewhere where new users who are reading through help could notice it.)
I think that it is useful to know that apart from the built-in search it is possible to use also some external search engine to search on this site. Specifically, I think it would be worth mentioning that it is possible to use Google with parameter site:math.stackexchange.com. And Approach0 seems to be very useful for formulas. (I am less sure whether also possibility to "search through ask dialogue" should be mentioned, although this is quite useful in some situations, too.)
Another possibility would be to make a dedicated faq post on meta collecting basic information about search - and then add a link to this post. But this would probably be less efficient that directly adding this information in the help center - since it is less likely that somebody displays information if they need to click and go on another page to see it.
Another question is that if we decide that this information should be added somewhere, what would the right place for it be. It me the part of help center dedicated to searching seems like a reasonable place: How do I search?
In the help on asking questions it is mentioned that users should search first. This gives a link directly to the built-in-search. In fact, this link is given there twice. Would it be perhaps reasonable to change one of those two links to https://math.stackexchange.com/help/searching? (Especially if we add the information about other possibilities for searching to the latter.)