Enhancement: Add Typescript support to Searchbox libraries

**Is your feature request related to a problem? Please describe.**
A clear and concise description of what the problem is. Ex. I'm always frustrated when [...]

**Which libraries does this apply to.**
- [x] React
- [x] Vue
- [x] React Native

**Describe the solution you'd like**
Users using Typescript can't use these libraries without Typescript bindings. There's a user who requested this for React Native Searchbox: https://github.com/appbaseio/reactivesearch/discussions/1713.

**Describe alternatives you've considered**
A clear and concise description of any alternative solutions or features you've considered.

**Additional context**
Add any other context or screenshots about the feature request here.

Start by locating the React, Vue, and React Native Searchbox library entry points and checking how their public APIs are currently exposed. The issue is complete when each of the three libraries has usable TypeScript bindings, but it does not identify files, tests, or a more specific implementation scope.

Written by the indexing model from the issue text.