[Feature Request] Allow programmatic (+ atomic) full reindex / import

- Symfony version: 5.0+
- Algolia Search Bundle version: any
- Algolia Client Version: any
- Language Version: any

### Description
It would be really great if you could extract the logic in `SearchImportCommand` into a separate service, so that one can easily do an atomatic full reimport programmatically. Currently you have to manually build fake CLI arguments and call the command, which is quite awkward (or copy & paste the complete code, which is just as awkward).

### Steps To Reproduce
n/a

Start by reading the SearchImportCommand and trace how it currently performs a full import from CLI arguments. Identify the reusable entry point needed for programmatic use and clarify how the atomic full reimport should be verified; done means callers can trigger the same operation without constructing fake CLI arguments.

Written by the indexing model from the issue text.