Update react_on_rails to 16.2.0.beta.13

Update the react_on_rails gem from current version to 16.2.0.beta.13.

## Tasks
- [ ] Update Gemfile to specify `react_on_rails` version `16.2.0.beta.13`
- [ ] Run `bundle update react_on_rails`
- [ ] Test the application to ensure compatibility
- [ ] Update any related documentation if needed