Which Apple Watch model can correctly count steps when I'm walking with a stroller and have both hands on the handle?

I’m not sure where you heard/read that a Series 8 Apple Watch or newer counts steps when pushing a stroller, but it doesn’t accurately for most people. Accuracy improves if you only use one hand to push it. It also improves if you manually select a Workout such as Outdoor Walk.

Apple Watch uses an accelerometer and gyroscope to measure the movement and compute steps. If the arm doesn’t swing, the stride and steps are not accurately detected. If this is important for you, I’d buy a pedometer and place it in your pocket. When the walk is completed, manually add the data to your Health app.