Setting Indexed column does not work

Question

We have a document library in a classic team site with many items (>5000) and three content types.

Regardless of the way setting an index on field "ContentType" - via UI (List Settings -> Indexed columns -> Add index -> Content Type), CSOM / Powershell (field.Indexed = true) - it shows the index in the UI but internally the content type field does not get indexed but the field "ContentTypeId" - unfortunately all queries using the filter on Content Type fail with a threshold error.

We have two other libraries using the same content types and set the same indexes and in both the index is working as excpected.

Is there any way to force the index creation or to find out why it is not used?