Let's take the demo store as an example. The "All products" link in the main menu returns a page where we can do searches base on facets. So we create an Index type server and there we add what fields we need to use in our facets.

The thing i was asked to do is to have these facets search in the taxonomy term pages. Is there a way to do this thing?

Perhaps with a contextual filter in the view that reads the term id or something like that. Can you please give me a direction to achieve this?

Here is a store that use what i need to do. It's not drupal commerce store but you'll get the idea

Demo store

Thank you in advance