sqlproxyccl: simplify NewSubStopper

[jeffswenson]

The lock in NewSubStopper caused lock ordering warnings when run under deadlock detection. The justification given for the lock's existence is wrong. If a closer is added to an already stopped stopper, the closer is called immediately.

Release note: None
Part of: #106571

[blathers-crl]

It looks like your PR touches production code but doesn't add or edit any test code. Did you consider adding tests to your PR?

_{🦉 Hoot! I am a Blathers, a bot for CockroachDB. My owner is dev-inf.}

[cockroach-teamcity]

This change is 

[jaylim-crl]

Reviewed 1 of 1 files at r1, all commit messages.
Reviewable status: complete! 1 of 0 LGTMs obtained (waiting on @darinpp)

[jeffswenson]

bors r+

[jeffswenson]

bors r+

[craig]

Build succeeded:

• Bazel Essential CI (Cockroach)

[blathers-crl]

Encountered an error creating backports. Some common things that can go wrong:

1. The backport branch might have already existed.
2. There was a merge conflict.
3. The backport branch contained merge commits.

You might need to create your backport manually using the backport tool.

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error setting reviewers, but backport branch blathers/backport-release-23.1-107316 is ready: POST https://api.github.com/repos/cockroachdb/cockroach/pulls/107972/requested_reviewers: 422 Reviews may only be requested from collaborators. One or more of the teams you specified is not a collaborator of the cockroachdb/cockroach repository. []

Backport to branch 23.1.x failed. See errors above.

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_{🦉 Hoot! I am a Blathers, a bot for CockroachDB. My owner is dev-inf.}