ccl/sqlproxyccl: TestConnectionMigration failed

ccl/sqlproxyccl.TestConnectionMigration [failed](https://teamcity.cockroachdb.com/buildConfiguration/Cockroach_Ci_TestsAwsLinuxArm64_UnitTests/21217540?buildTab=log) with [artifacts](https://teamcity.cockroachdb.com/buildConfiguration/Cockroach_Ci_TestsAwsLinuxArm64_UnitTests/21217540?buildTab=artifacts#/) on master @ [003732594082f2cbc933e90dd08e77258ad51414](https://github.com/cockroachdb/cockroach/commits/003732594082f2cbc933e90dd08e77258ad51414):

```
=== RUN TestConnectionMigration
test_log_scope.go:172: test logs captured to: /artifacts/tmp/_tmp/5d831302e446252f630c56f4e52acade/logTestConnectionMigration519735350
test_log_scope.go:82: use -show-logs to present logs inline
proxy_handler_test.go:2359: -- test log scope end --
--- FAIL: TestConnectionMigration (25.69s)
=== RUN TestConnectionMigration/transfer_timeout_in_response
proxy_handler_test.go:2333:
Error Trace: pkg/ccl/sqlproxyccl/proxy_handler_test.go:2333
Error: An error is expected but got nil.
Test: TestConnectionMigration/transfer_timeout_in_response
--- FAIL: TestConnectionMigration/transfer_timeout_in_response (10.04s)
```
Help

See also: [How To Investigate a Go Test Failure \(internal\)](https://cockroachlabs.atlassian.net/l/c/HgfXfJgM)

/cc @cockroachdb/sqlproxy-prs

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Jira issue: CRDB-61276