storage: fix shutdown token for copy to s3 sink

[benesch]

The COPY TO S3 sink must not flush files to S3 during shutdown, as those
files may only be partially written.

This can cause correctness issues when running copy operations on
multiprocess replicas, as the lagging replica's copy sink will get
dropped partway through.

Motivation

• This PR fixes a recognized bug.

Tips for reviewer

This is essentially just a copy of #30844, but I didn't want to lose my in progress CI run over there.

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.

[benesch]

Closing in favor of #30844.