Yes, this is great!

Please consider algolia for search components too, they have a react-native lib

Highly desired! 👍

Elastic Search may be suitable... https://github.com/elastic/elasticsearch

Not sure if Algolia would be a great way to implement this

I guess the usual and expected behaviour of all search boxes across the internet (and all local search boxes on all devices I have seen) would be searching by all data available.

Like, if there is list of records from a collection, that comes with search, then expected behaviour is that it would search everything in that collection, all fields available, not just one.