I rebuilt the engine successfully, but the project won't compile.

I have a project made with 4.72 Engine version that is downloaded with the Epic Editor. And it works just fine.
I downloaded the source code from Git of the same version 4.27 to edit some aspects of the engine code.
The engine was built successfully, and I made a test project with it and it worked fine.

However, I can’t build the main project to work on the edited version of the Engine. I deleted VS files, Saved, and Intermediate files, regenerated VS code, built the project in IDE successfully (with a strange very quick building about 3 seconds?). But then whenever I open the editor to run the project, it keeps telling me that it needs to be rebuilt. Then asks me to rebuild it from the IDE, which I already did. Rinse and repeat, and never works.

Did you try changing the engine version of the project? If you right click the uproject file in Windows Explorer then select “Switch Unreal Engine version…” a small dialog with a dropdown and a folder browser button should open. Select the engine built from source in the dropdown or use the folder browser to navigate to it if it isn’t the correct version yet. Then try regenerating the solution and build the project again.