Instead of start of “C:\Program Files\Duplicati 2\Duplicati.GUI.TrayIcon.exe”, could you try starting the 2.0.5.1 Duplicati.GUI.TrayIcon.exe directly? Also, what version does Program Files changelog.txt say?
Update design puts the updates in a different location which doesn’t require Administator permissions.
Downgrading / reverting to a lower version shows several places to inventory for installed updates, e.g.
C:\Users\<Duplicati user account>\AppData\Local\Duplicati\updates
C:\ProgramData\Duplicati\updates
and I say that not to encourage downgrade, but to debug this upgrade issue by looking at old versions.
There may be something on some systems that does it. Both you and I have seen 2.0.5.1 starting fine.
The link from @drwtsn32 includes some explanations from me on the unusual way that updates work. Although I’m not a .dll expert (I hope someone else is), I think Newtonsoft.Json just went from 10 to 12, however the old Program Files one should have used 10, and the 2.0.5.1 update should have found 12.
Your start of 2.0.5.1 directly will probably go 12 initially for parent and child (both on 2.0.5.1), and if that works, then uninstall and reinstall from .msi will put Program Files on 2.0.5.1 and maybe all will be well, however if you can help with figuring out where this is going wrong, narrowing it down would be helpful.