Adding a non-Steam game through the "Browse.." menu - i.e. when you're navigating through the Windows file explorer rather than through the list of programs Steam shows initially upon clicking "Add a Non-Steam Game" - does not work. It does not appear in the list of programs, or in the library after selecting any executable.

Windows 11 Pro Build 22621.1555

Click "Add a Game"
Click "Add a Non-Steam Game..."
Click "Browse.."
Navigate to any executable file; even one that is listed in the initial Steam modal that pops up.
Click the executable file, then click "Open"

The "Browse" window closes, and the initial list of non-Steam games remains unchanged.

The executable file I selected in the "Browse" menu appears in the list of non-Steam games, and is checked. When I then click "Add selected programs", the selected executable appears in my library and can be launched through Steam.