Stage Manager activated but does not appear in Control Center

I had a similar problem. Make sure that the System Settings / Desktop & Dock the 'Displays have separate Spaces' option is turned ON. After logging out then back in the Stage Manager menu toggle showed the Stage Manager option, and the Desktop & Dock Stage Manger on/off Customize... was no longer greyed out and yes, Stage Manager now works.

LongTimeiMac wrote:

My Stage Manager activation (show in menu bar) does not appear and is ghosted in System Settings and cannot be selected. It appears to be present but does not appear in the Control Center.

Stage Manager on Mac: How it works in macOS Ventura

ref

Organize your Mac desktop with Stage Manager - Apple Support

Use Stage Manager to organize apps and windows on Mac

Move, resize, and organize windows with Stage Manager on ...