How do I get a project to show up in the Project Browser?

Natigate to:

%LOCALAPPDATA%\UnrealEngine\5.4\Saved\Config\WindowsEditor
replace 5.4 with a version of the engine that your project is created with
then open EditorSettings.ini file.
Add path of a folder that your project folder located in, for example if your .uproject file is inside
C:/Parent/ProjectName
add
CreatedProjectPaths=C:/Parent under [/Script/UnrealEd.EditorSettings] section