Well although the FHS is somewhat out-of-date (as it doesn’t e.g. account for the /usr merge), the systemd filesystem hierarchy specification does say:
Vendor-supplied operating system resources. Usually read-only, but this is not required. Possibly shared between multiple hosts. This directory should not be modified by the administrator, except when installing or removing vendor-supplied packages.
This is why package managers generally have a fit if you do anything inside /usr itself that they haven’t tracked. (Also why you should never use
sudo pip, because it does try to write here and has a tendency to overwrite system Python libraries with incorrect versions.)
/usr/local, on the other hand, generally should be RW (and it is on Silverblue), since that’s where system-global installations that are not managed by the package manager should go.
Based on both the FHS and the systemd specification, NoMachine should write logs to /var and configuration data to /etc or /var/lib.