I noticed this on OpenAI docs:
It’s a reasonable compromise, it “looks like search”, “it feels like search” but it is just launching a modal.
I think it is a great compromise to a concern @hugh raised, the downside of having this as a box on top is that there is lots of thinking needed to figure out how to render in sidebar, if we don’t, it takes you away from where you are which is surprising.
However this solution on the docs page feels very natural, plus you don’t navigate away it simply shows the modal.