How to index Drupal Commerce 2 products for the search?
The core search will only ever search node's and users. If you want to search other entity types, like products, use Search API.

Just install the module, create a server (you can use the search api db submodule if you just want to use your sql database) and create your index. You will have the option of selecting which entity types get added to the index, you probably want nodes and products. Then add which ever fields that you want to be searchable. 

See the official documentation for screenshots and more info on how to take it further (like adding facets).