How can I make Search API search field collections?
You shouldn't use the field collection module in D8 to begin with, as the project page says



and it also says

Drupal 8
Use Paragraphs and Entity Reference Revisions instead of field collection for Drupal 8 projects.

If you don't make the change now you will have to, in the future, whenever you migrate to D9 as there won't be any D9 version.