I'm running Windows 11 Pro 22635.4300 with ObjectDock 3.0.1.4, and I don't see the lag you're talking about. If I set the dock position at the top and set Accessibility to Autohide and the far left position of Short delay, the dock pops up immediately. It's actually faster than the Autohide taskbar. Same response for tabbed docks.
I'm not sure what other setting you are using. I'm not showing running applications, and I only have 21 shortcuts on my dock.