Can the App manage / access onboard-logs?

No! Both log types are completely independent in terms of setting, speed, and storage location.
For example an onboard-log can be set to start at 10kN load and record for 1 minute.
A second log can be started and stopped e.g. manually in the app while this onbaord-log is recording.
The onboard-log will be stored in LS3 memory, the app log will be stored on the smart phone.
It is not possible to access the onboard logs via the App!
Onboard logs can only be downloaded from the LS3 by plugging in a USB flash drive.