Given Docker being available on (certain models?) of Synlogy NAS, it might cover more bases to create a docker container for the ManicTime server, rather than one specific to Synology.
I think the most accurate thing to do is to record both the remote desktop session and the remote machine, but only count activity on the remote machine when the remote desktop session is active.
This also has the benefit that you can re-process previously collected data to produce a more accurate result.
I thought that previously there was already support (in the pro version) for collecting and storing data in (say) OneDrive on multiple computers, then using any of the clients to summarise the collected data.