There is no web searching tool in the world that will match Google. They'd have the best engineers and analysts in the field working to improve their algorithms.
Pokemaster himself may update you on whether the search function is a priority in Q2A's development right now. But, for now, the best way to improve your search results is to make smarter searches. If you're used to using Google, then you can use their search operators to limit the results to PokeBase and force particular phrases to appear in the results, among other things. Try searching
"battle stadium" site:pokemondb.net/pokebase -rmt on Google as an example.
If you are to continue using PokeBase's search bar, then bear in mind how it works and what it prioritises. It doesn't read English, so put keywords into it instead of sentences. It values recency above all else, and it likes popular posts. It seems to prioritise posts with tags that match the words you put in the search query. Questions that contain search terms in their body or within their answers do appear, but tend to fall down the pecking order. Use this information to inform what you put into the search box.