Originally raised in #58551 (comment)

Problem Description

With PDEP-14 there is the need for developers to be aware of the storage used for strings. Indeed, the storage might have a lot of impact of performance, for instance

• pyarrow storage
  • pros: compact (optimal memory footprint), fast (vectorization)
  • cons: immutable (so any modification creates a new string pyarrow ChunkedArray)
• python storage
  • pros: mutable
  • cons: highest memory footprint (each string is a different Python object), slow (no vectorization)
• numpy 2.0 strings storage (I don't have a good knowledge of these new strings, and never tested them)
  • pros: compact, vectorization, mutable (my understanding is that is takes more space and is slower than pyarrow strings)
  • cons: different representations depending on a string size, which make understanding performance harder

Feature Description

I would like to have two way to discover the storage

• __repr__ goal is to give information on the inner of an object, one option suggested by @jorisvandenbossche is to display <pandas.StringDtype(storage=...)> instead of string[storage]
• .get_storage that returns the storage (not sure what is possible with the current implementation, would be best to have a class, otherwise, a string). The API is useful to check before running a time consuming code that we have the correct storage.

Alternative Solutions

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Additional Context

No response