The general public have no issue saying a computer is thinking when you’re sitting there waiting for it to calculate a route or doing a similar process like selecting a chess move.

The connotation is simply an internal process of indeterminate length rather than one of reflexive length. So they don’t apply it when a GPU is slinging out 120 FPS in a first person shooter.

That's right when saying selecting not calculating a chess move - assuming you are outside of Plato's cave (Popper).

But now, I see this: the truth is static and non-profit, but calculating something can be sold again and again, if you have a hammer (processing) everything looks like a nail, to sell well the word thinking had to be used instead of excuse for every time results being different (like the shadows) - then, we can have only things that let someone else keep making profits: JS, LLM, whatever.. (just not.. "XSLT" alike).

(yet, I need to study for your second sentence;)