When configuring syslog aggregate drain to forward all application logs to Dynatrace, start/stop events are not considered logs. Therefore, this is expected behavior, and by default, it only forwards LogMessage envelopes.
To send additional information like 'HttpStartStop', add a parameter to the end of the syslog drain url that is configured in the tile.
Ops Manager → TAS tile → System Logging → Aggregate syslog drain destinations
syslog://####.####.####.com:601?include=all