If anyone is curious, this is how it looks so far, after a couple of evenings of fixing.
It launches (barely, still with some errors), but many systems are completely broken.

Must have

• Fix any immediate blocking problems (script parsing errors, etc.).
• Verify core functionality and fix if needed:
  • Game installation.
  • Game launching.
  • Handling of multiple game installations.
  • Mod installation and management.
  • Soundpack installation/deletion.
  • Font customization.
  • Backups.
• Fix localizations.
• Fix tab disabling method in Tabs.gd (or find an alternative).
• Fix stable/experimental selection UI.
• Fix appearance of custom icon buttons.
• Revisit OSExecWrapper and decide what to do with it.
• Fix invisible scroll bars.
• Fix visual issues in themes.
• Fix icon scaling.
• Fix font scaling.
• Fix any other issues with theming.
• Playtest on Linux.

Nice to have

• Modernize code according to changes in Godot 4 (new getter/setter syntax, typed arrays, callables, etc.).
• Zipping and unzipping can now be done by Godot itself. There is no need to rely on external commands or exe's anymore.
• Update game launching.

Extra ideas (can be done later)

• Centralize duplicated JSON loading code that exists in many places.
• Add a new theme based on Godot 4 editor theme.
• Create a watchdog for the game process that will track if the game is running.

UPD. 25/10/25: Some more blocking issues discovered:

• Ingame font files are not getting exported.
• Linux: New symlinks were added to releases of several forks, causing Godot issues with file operations. Need a more robust solution.

While trying to work on #182 , I opened the project in Godot 4 (I was not aware this project was done in v3). Wow, this seems like a huge task. Ill take a look at your godot4 branch on some spare time and see if I can help.