Apple have both a USB-C to VGA and Lightning to VGA Adapters compatible with appropriate models of iPad:
- USB-C VGA Multiport Adapter
https://store.apple.com/uk/xc/product/MJ1L2ZM/A
https://store.apple.com/uk/xc/product/MD825ZM/A
As for Stage Manager, this is a feature of iPadOS16 - currently in beta. Until iPadOS16 is released as a production version, it is impossible to offer definitive comment as to what (if any) support will be available for specific monitor interfaces. Perhaps consider that VGA is a very old analogue (legacy) video standard, superseded by HDMI and DisplayPort digital interface standards.