Please flesh out documentation for installation & use on Linux

I don’t think there’s any game to this. Just like Java, C# generates portable bytecode that’s interpreted later.
Duplicati is the old web site for version 1 showing last release “on 2013-02-02 for Windows, Linux, MacOS” Duplicati 2 has also always been portable AFAIK. Admittedly, usage statistics tilt towards Windows though.

They exist there when they’re .NET assemblies.

.NET, metadata, and the PE format (Wikipedia)
.NET Assembly File Format (Microsoft)
Introduction to developing with Mono Assemblies
Can I run Mono applications without using ‘mono program.exe’? shows a way to get transparent running of an .exe similarly to how Windows runs the .NET Framework transparently when you run a .NET assembly, however it then advises not to do that, but to use a wrapper script instead. Duplicati has several wrappers:

$ whereis duplicati
duplicati: /usr/bin/duplicati /usr/lib/duplicati
$ which duplicati
/usr/bin/duplicati
$ head -2 /usr/bin/duplicati
#!/bin/bash
INSTALLDIR=/usr/lib/duplicati
$ file /usr/lib/duplicati/Duplicati.CommandLine.exe
/usr/lib/duplicati/Duplicati.CommandLine.exe: PE32 executable (console) Intel 80386 Mono/.Net assembly, for MS Windows
$ 

I’m not sure if Linux and MacOS locations for Duplicati are completely standardized, and distributions can presumably package Duplicati to fit whatever the OS convention is, so it’s hard to document what they do. Locations for common system types could probably be said, but Windows is simpler (yet undocumented).

Using Duplicati from the Command Line
Other Command Line Utilities

All Command Line Utilities can be found in the Duplicati program folder.

is probably the sort of statement that could be expanded further (including for Windows), and the need to run mono could be said more widely. It’s sort of said below, but then it doesn’t cover the directory to be in

How to use the Duplicati Command Line tool

Linux and Mac OS X users should type mono Duplicati.CommandLine.exe or duplicati-cli , which is a wrapper for running mono Duplicati.CommandLine.exe .

I’m not sure if there’s much hope in the near future for installation directions on every sort of Linux around.
The How-To category of the forum covers some. Maybe when stable enough, some can go in the manual. For reliability there might need to be verification of the draft by some person who actually has that system.