Still no manual
I don't see a manual in Steam. (Right clicking on the game and selecting properties shows "Manual: [none available]".)
I also don't have a manual.pdf file. (The only Sins of a Solar Empire folder I have is in AppData, with no PDFs.) Either Steam changed the distribution, or that answer refers to the Stardock distribution.
I was able to find a manual online. Searching Google for "Sins of a Solar Empire Training Manual" (in quotes) seems to give the best results. Some of the sites may not be entirely legitimate, so use care when clicking.