Sorry to hear you had that much trouble getting things running. FYI, the “Generate Visual Studio project files” context menu in windows explorer is provided by the UnrealVersionSelector.exe application and comes with the Epic Launcher, not Unreal Engine. So if you install Unreal Engine via the Epic Launcher, it’ll set up the correct paths and configuration for you. But if you build from source, it won’t set it up.
To fix the menu, you can copy the UnrealVersionSelector.exe from:
C:\Program Files (x86)\Epic Games\Launcher\Engine\Binaries\Win64
to your UE install:
C:\Program Files\Epic Games\UE_5.0\Engine\Binaries\Win64
And then run the exe from there to register it. Select Yes and it should be fixed.
For the .uproject file, you can right click and “Open With” → “Choose another app” → “More Apps” → “Look for another app on this PC” and select the exe in your UE install that you copied. Make sure “Always use this app” is checked.