Do moto gp bikes have such complex suspension? Or Paris Dakar bikes?
They tend to be linkage driven single pivots. With the pivot behind the drive sprocket an inch or two below the chain.
Because chain tension on a motorbike is approximately constant (an I4 engine with 360deg firing order at 10,000rpm is 333Hz, a cyclist is ~ 1.5Hz). So you open the throttle and the suspension compresses slightly because at the same time the rider will be throwing their weight over the front of the bike to stop it wheelieing.
A push bike you push down on the pedal and the last thing you want is the bike to squat down away from you, so you add linkages (or raise the single pivot and typically have it much more inline with the drive sprocket or infront). This means as you push down on the pedal the bike squats, which tries to lengthen the chain which the pedaling counteracts pushing the bike back up again.
The objective being that the push-bike is in the same shape at the start of the pedal stroke as at the end. A Motorbike only needs to deal with making the bike behave itself (grip, handling) as at the frequency it operates the suspension doesn’t move.
Unless you start looking at ‘big bang’ engines and V-twins/V-four, which are deliberately designed to bounce the rear tyre on the road giving you a burst of acceleration which breaks traction, but then a recovery which makes it more predictable and controllable. Which is why you won’t see an i4 engine in a Dakar style bike, it could have more power, but wouldn’t have grip.