Hi there,
I would double check the visual studio installation, along with following these steps to see if you missed anything: Building Unreal Engine from Source | Unreal Engine 5.2 Documentation
Not familiar with the project you linked; so apologies if there is something there causing it I doubt it though. Most likely some kind of module is missing.
Another option: make sure the project has the right build configuration (e.g. x64 and Development Editor) within Visual Studio.
One last thing - this post sounds similar. Anything you can find there that may give you a clue? Compiling UE 4 first time - Unable to read module manifest - #8 by eco_bach2
Wish I could give you more specific direction. I’ll give it some more thought.