[analysis_server] Fix recording of completion timings in LSP completion handler

Change-Id: I6dbb0aa7a3598c816407c8354408ba0795387d0d
Reviewed-on: https://dart-review.googlesource.com/c/sdk/+/240406
Reviewed-by: Brian Wilkerson <brianwilkerson@google.com>
Commit-Queue: Brian Wilkerson <brianwilkerson@google.com>

Author: DanTup