[persist] Remove some usage logic that depends on the writer id

[bkirwi]

Motivation

Since we never write blobs with the writer id prefix anymore, all blobs with that prefix are either present in the state or leaked. Here we simplify some checks and update some tests to use the simpler writer key comparison.

(We're thinking about changing the writer key format yet again; nice to clean up some logic related to the old format before possibly adding another one!)

Checklist

• This PR has adequate test coverage / QA involvement has been duly considered. (trigger-ci for additional test/nightly runs)
• 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).
• If this PR includes major user-facing behavior changes, I have pinged the relevant PM to schedule a changelog post.

[ParkMyCar]

LGTM!