[GUI] The directory selection menu does not work with the Web disabled

[guglovich]

Your system information

• Steam client version (build number or date): 27.06.22
• Distribution (e.g. Ubuntu): Arch
• Opted into Steam client beta?: [Yes/No] Yes
• Have you checked for system updates?: [Yes/No]

The directory selection menu does not work with the Web disabled. The client must have removed the native counterpart when they made the new menu on the Web.

Peek 2022-07-15 02-35.webm

Steps for reproducing this issue:

1. Run the client with the no-browser option