As Steam's Proton compatibility tools places every Windows running program installed by Steam into their own separate windows-replicating folders named by the program's [APPID], information is, in our scope of information details, isolated from one-another.
When applied in to the context of Cell Command, Cell Command [3362040] is unaware of Cell Command Demo's [3364450] existence, let alone save data, because they are stored in different folders.

Thus, Cell Command's Demo save data will need to be manually copied to the Cell Command location. A standard copy-paste action.

All files involved are contained in the SteamLibrary folder that, if multiple exist, you explicitly selected when you installed the game. The default location will vary depending on how you installed Steam (AUR, DEB, FLATPAK, etc.)
You likely already know where this is stored but if not, two quick ways to find out are as follows:

• (Method 1) Library ➜ Cell Command / Cell Command Demo ➜ Right Click / Click ⚙️ ➜ Browse Local Files
  This should hopefully open your file manager at the location of the game's install location. These files are NOT the save files but you do now know know where and what the relevant SteamLibrary folder is.
  Navigate up from Cell Command / Cell Command Demo and up from common. You should be at the SteamLibrary/steamapps folder
  
  
• (Method 2) Steam Settings ➜ Storage and clicking on the dropdown list of SteamLibrary paths and then finding Cell Command / Cell Command Demo
  Open up your file manager and navigate to that path and access the SteamLibrary folder

Copy both folders from Cell Command Demo [3364450]'s Alpherior folder to Cell Command [3362040]'s Alpherior folder. Overwrite all files.

Once done, launch Cell Command. The game, now aware of the Demo's data, will copy over the savedata to the main game as it would normally on Windows. Along with achievements from the Demo becoming registered for the full game.
And that's it! The Demo can now be safely uninstalled.
Happy commanding!