I believe you have a 1968 Massey 2200. The photos were taken too close to the machine to make a definitive decision. The 2200 was a weird creature available as an industrial tractor, backhoe, forklift and forwarder (treever). So you have to be careful getting parts as they differ in many aspects. It is not a 2135 as the 2135 did not have a hardnose and required a front support for the loader as shown in the first photo on tractordata. It is most defiantly an industrial model as it has a hardnose. Your guess was close with the 135 orchard as the 135 orchard used the 2135 industrial front axle 192019M92 and other steering components as a cost savings measure by MF. MF 2135 and 135 orchards are difficult to tell apart at a glance due to the commonality, however you do not have one. The ability to move the wheels left and right by hand with the tractor running is concerning.
You could have a cylinder that is completely toast letting the fluid bypass. I would lift the front end up and support it so the wheels are free. Then I would turn the wheels all the way one direction. Take the hose off of the rod end of the outer cylinder plug the hose and then turn the wheel more to see if fluid comes out of the cylinder. If it does then the cylinder is bypassing internally. Check the other side then.