Question about wildcard query

[anyla]

Furthermore, If I create another index with the same field but this time using a custom analyzer (standard tokenizer + stop filter), then the query with

GET my_test2/_search
{
  "query": {
    "wildcard": {
      "test_test": {
        "value":"*Butterflies*"
      }
      
    }
  }
}

Does not return any hit, which leads me to think that the search term is analyzed.

I found in this post a user with a similar situation

Wildcard search case insensitive

So in short. When you index a field with a text type and default analyzer, it is indexed in lowercase and broken into tokens. Aaa Bbb became aaa, bbb. When you search with a wildcard query (which is a bad idea), you must use the same case as was indexed. So aa* should work where Aa* shouldn't. For keywords, they are indexed as Aaa Bbb, so searching for Aa* will match. Note that Bb* won't match. With a lowercase normalizer, aa* will match. Aa*, Bb* or bb* won't match.

Look at the 2nd and 4th posts. I don't know if @dadoonet found the explanation for that case

Thank you
Regards
Ana