Search doesn't work for simplest cases

**Your Godot version:**
4.71.

**Issue description:**

I would expect the documentation search to show me the PhysicsBody2D documentation when I search for "PhysicsBody", but only when I spell out the whole type it works. This is really frustrating and not a usable search in 2026. Most frustrating is that the search in older godot documentation versions worked perfectly, why was this changed to a significanly inferior version of search?
Searching for a specific full method name also simply doesn't work.
\
I would suggest that we rollback to the previous search.

\

**URL to the documentation page:**
https://docs.godotengine.org/en/stable/
Specific page doesn't matter, it's about the search.

Start at https://docs.godotengine.org/en/stable/ and reproduce the reported searches for "PhysicsBody" and a specific full method name. Compare the current results with the older documentation search behavior described in the issue; done means partial class and method searches return the relevant documentation pages.

Written by the indexing model from the issue text.