I'm indexing just fine. Edit mode search works etc. Using 13.6.0 versions.

SERP needs to send locale but then no media items are included in the results.

A simple query to check with where results show all these three locale fields as empty:

{
  _Media(
    locale: ALL
      where: { 
       _assetMetadata: { mimeType: { eq: "application/pdf" } }
  }) {
    total(all: true)
    items
    {
      _assetMetadata
      {
        mimeType
      }
      _metadata
      {
        locale
        locales
        fallbackForLocale
      }
    }
  }
}