basalt-26.3: crosscluster/logical/txnmode: TestTxnModeLWW failed

crosscluster/logical/txnmode.TestTxnModeLWW [failed](https://mesolite.cluster.engflow.com/invocations/default/376fcf97-274a-4e7c-ad0a-4aafab7d24f7?testReportRun=2&testReportShard=3&testReportAttempt=1#targets-Ly9wa2cvY3Jvc3NjbHVzdGVyL2xvZ2ljYWwvdHhubW9kZTp0eG5tb2RlX3Rlc3Q=) on basalt-26.3 @ [c6d01ae4be9708178b248a49819b505daf713377](https://github.com/cockroachdb/cockroach/commits/c6d01ae4be9708178b248a49819b505daf713377):

```
=== RUN TestTxnModeLWW
test_log_scope.go:172: test logs captured to: outputs.zip/logTestTxnModeLWW620734375
test_log_scope.go:82: use -show-logs to present logs inline
test_server_shim.go:168: automatically injected a shared process virtual cluster under test; see comment at top of test_server_shim.go for details.
=== RUN TestTxnModeLWW/transactional
```

Parameters:
- attempt=1
- race=true
- run=2
- shard=3
Help

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

/cc @cockroachlabs/cdc

[This test on roachdash](https://roachdash.crdb.dev/?filter=status:open%20t:.*TestTxnModeLWW.*&sort=title+created&display=lastcommented+project) | [Improve this report!](https://github.com/cockroachdb/cockroach/tree/master/pkg/cmd/bazci/githubpost/issues)

Jira issue: CRDB-68095

Start with the linked test report and its captured logs for crosscluster/logical/txnmode.TestTxnModeLWW at commit c6d01ae4be9708178b248a49819b505daf713377. Reproduce the failure with race=true, run=2, and shard=3, then identify the cause and make the test pass reliably.

Written by the indexing model from the issue text.