If the migration re-created (export/import) categories/tags or any other taxonomy terms, and if you use any exclusion/inclusion based rules then it’s probably that, because in that case the term IDs change.
Usually the best start off point is to create a new search instance to see if that works, it very likely should if you have any posts/pages by default – and then try to recreate the configuration via that.
If nothing works, you can add temporary back-end details and I will check the configuration.