Cirlcing back to update…
I purchased the Apple 27" Studio Display and there is no longer a problem. The display wakes up instantly–just the way the Apple Cinema Display wakes when used on the Intel MacPro.
It’s difficult to determine the root cause of the problem: it could be the display, the adaptor, or the M2 Studio. But I also had issues with an older Apple USB keyboard with the M2 Mac Studio so there may be reasons to believe that Apple Silicon is not fully compatible with legacy Apple products.