perf: API docs: fix needless rerendering of page

Created by: slimsag

This was incredibly difficult for me to track down, probably 9h of my time overall. See #21200 (closed) for details.

We'll need to apply this same fix to other pages in this routes.tsx file, because they are 100% affected by this. Also, this isn't a complete fix - there are other issues (like not using React.memo on this page) that mean typing in the search bar is still incredibly sluggish.

Helps #21200 (closed)

Signed-off-by: Stephen Gutekanst [email protected]