Why there is no stage manager in iPad air 4th gen !?!?

Due to limitations of internal hardware, the new Stage Manager feature introduced with iPadOS 16.1 is only available for these models of iPad:

• iPad Air (5th generation)
• iPad Pro 11-inch (all generations)
• iPad Pro 12.9-inch (3rd generation and later)

Feature availability is usually limited by system hardware - CPU and available RAM being critical to some advanced functionality.

iPad models supporting Stage Manager have an M2, M1 or A12X CPU (upon which the M-series CPUs are reportedly based) - with at least 8GB RAM. The iPad Air4 has only 4GB RAM.

Whether or not a functionally limited version of Stage Manager, compatible with models of iPad that do not meet the current hardware requirements, will ever be released is unknown.

Only Apple would know the answers to those questions. But, at a guess, I say hardware limitations prevent it from being offered on the iPad Air 4.