Search with Algolia Bogo extension

PMF

The facet has not the locale attributes!

Probably you have been created the indices before activate the plugin.
You need to delete the indices and re-index it.

Or, you can manually add the facet in the Algolia dashboard.
https://www.algolia.com/doc/guides/managing-results/refine-results/faceting/

How can we search by the locale attribute?

You can search by the following query.

index.search("", {
 "getRankingInfo": true,
 "analytics": false,
 "enableABTest": false,
 "hitsPerPage": 10,
 "attributesToRetrieve": "*",
 "attributesToSnippet": "*:20",
 "snippetEllipsisText": "…",
 "responseFields": "*",
 "maxValuesPerFacet": 100,
 "page": 0,
 "facets": [
  "*",
  "locale",
 ],
 "facetFilters": [
  [
   "locale:en_US"
  ]
 ]
});

When the Bogo plugin deactivated, what the behavior will changes?

Bogo will put the _locale attributes into the post_meta, and the plugin uses it.
So the plugin still put the locale attributes if exists.

But, if the post has no _locale post_meta attribute, the plugin does not put the locale attributes.