Hi
For all that still don’t see the projects under “recent projects” in the project browser either due to moving projects to another folder/drive for what ever reason.
Here is the fix I found.
C:\Users(user)\AppData\Local\UnrealEngine\5.1\Saved\Config\WindowsEditor
edit EditorSettings.ini
Look for ‘CreatedProjectPaths=’
Update the path to your new location.
It should now show all your projects in the recent project tab when you relaunch the editor.