Strang does include that. I just checked the fourth edition, like you say you did. Scrolling down two pages to get to the first page of the table of contents, I see the heading “cosines and projections onto lines”. I navigate to that section and it explains all the logic, proof, and intuition behind the connection between angles and dot products. Please don’t spread misinformation…

That's page 171, 13 dense pages into the section on orthogonality, long after he's introduced the dot product, in a section where he says, in italics, "the orthogonal case is the most important"; he gives cosines about half a page before going back to a perp b.

Nobody said Strang never mentioned cos θ --- that would be weird --- only that his sequencing doesn't treat the angle formula as fundamental, even in the section introducing it. And nobody has ever read Strang and thought projections didn't matter.