Is iPad 9th generation is stage manager compatible? Where can I get this compatibility list?
Stage manager device compatibility
This isn't really a question for the Developer Forums - this is where developers of apps communicate and ask for help on coding apps, not standard product support questions.
However, I've gone to the trouble of looking at the iPadOS 16 page on Apple's website, and it says Stage Manager is compatible with: Available on iPad Air (5th generation), iPad Pro 12.9-inch (5th generation), and iPad Pro 11-inch (3rd generation)."
So no, not your 9th-gen iPad.