api/proxy: preserve active connections after auth failure

[vigneshakaviki]

Description

Preserve active proxy connections when a new connection fails authorization. The authorization failure still closes the listener so no further connections can start, but it no longer cancels the shared context used by already-active connections.

Security-control impact: none. Authorization behavior remains unchanged; rejected connections still fail and stop the listener.

Closes #6774

Testing

• go test ./proxy -run ^TestStartAuthorizationFailureKeepsExistingConnections$ -count=20
• go test -race ./proxy -run ^TestStartAuthorizationFailureKeepsExistingConnections$ -count=1
• go test ./... -count=1 (from api/)
• go vet ./... (from api/)
• LINT_DIFF_BRANCH=origin/main make lint-diff

PCI review checklist

• I have documented a clear reason for, and description of, the change I am making.
• If applicable, I have documented a plan to revert these changes if they require more than reverting the pull request.
• If applicable, I have documented the impact of any changes to security controls.
  Examples of changes to security controls include using new access control methods, adding or removing logging pipelines, etc.