Welcome. Where abouts in Aus? I have been to the south and east several times, wonderfull places

As Greg suggested, Lift the front end and spin the wheels independently by hand. I think the opposite wheel spinning backward only reliably happens when 4WD is engaged(otherwise the driveshaft may spin). Do this from both sides, it should be smooth and quiet. You should also wiggle the wheels from side to side/top to bottom and look for any loose spindle action or play. Also a good idea while you are down there is to take a look under the rubber boot at the steering clevis and locknut to make sure it is all tight.
The 4WD engagement on the 200 series is shift-on-the-fly, no clutch required. When you lift that 4WD lever you are engaging two flat faced 3 tooth "claws" that are hard coupled to the axles. You could stomp on the clutch all day and you are not going to change this relationship or make the claws line up.
Since both these claws are linked to the axles, you need to be rolling to get a difference in claw RPM so their teeth line up. because of the difference in wheel size and gearing, they will both spin at slightly different speeds when rolling. Just hold gentle pressure up on the lever while rolling and when they align, the lever will fully engage. This could be a little stiff on a new tractor. After 2 years use, mine goes in and out with one finger on the lever.
Holding pressure on the lever while rolling(or while a rear wheel is spinning) is the same procedure used to engage the rear difflock. It also uses the same type 3 toothed claw to link the two rear wheels together and has to align to engage.