I’ve just released v0.1.5, which fixes the search and should improve this (this issue was bothering me too).
I found a solution that works well enough without clashing with their extension. You just need to use the Open Godot API Documentation command (default: CTRL F1; ⌥ ⌘ D on macOS) instead of going to the definition with F12. This shortcut works even in GDScript.
If you use this when the text cursor is on a word that looks like a class, it takes you to the docs page of that class. If it’s in another word or some other text that is selected, it takes you to the search page, searching that text; then you can try to find it.
This simply matches the word, it doesn’t analyze the code at all. You can still use F12 on GDScript to use godot-tools like before (which does analyze the code and can find definitions in non-obvious cases like when the class is implied).