storage: move some stuff from mz_storage_client::client to mz_storage_client::statistics

[guswynn]

Broken out of #25218

Motivation

• This PR refactors existing code.

Checklist

• This PR has adequate test coverage / QA involvement has been duly considered.
• This PR has an associated up-to-date design doc, is a design doc (template), or is sufficiently small to not require a design.
• If this PR evolves an existing $T ⇔ Proto$T mapping (possibly in a backwards-incompatible way), then it is tagged with a T-proto label.
• If this PR will require changes to cloud orchestration or tests, there is a companion cloud PR to account for those changes that is tagged with the release-blocker label (example).
• This PR includes the following user-facing behavior changes: