Searching through big DataList from API

Question

I have an app in which I want to show a list of around 19000 products. You can search this list and you can filter it by categories. I added paging for my API where the data comes from and I plan on using LoadMore for React FlatList. Now, when I type a search-query inside the search-bar, I want to search within all the data, not the filtered data. Where should I perform the search then? Should i either load all 19000 Items from the API, store them locally and search it? Then the paging would be kind of unnecessary.. Or should I send the search-term to the API and handle the search there? The latter also seems kind of inperformant, because It would send an API-Request every moment I type a letter to the search-bar. Or is there a third approach? What would be the proper way for this?

Thanks in Advance.