The joint should really be called a sacrificial contraction joint. Concrete is good at compressing, lousy at tension, which is the force that occurs in contraction. (That's why you put rebar in concrete, to compensate for this difficiency.) Either the joint clearly separates the slabs, with felt, wood, rubber or something in between. Otherwise, a slab gets a big score put across it by the mason, in some sort of hope the contraction cracks can be encouraged to happen in there. That looks much less nasty and is why I call it sacrificial. In your case, it was nice of the joint to separate rather cleanly along the joint, rather than breaking the slab into 5 jagged chunks! I'm kind of assuming the one slab was lifted by tree roots, as opposed to the other slab settling.
If you don't think the slabs are moving anymore, and you just want a short transition between them to make it less of a tripping hazard, I don't think I'd add a joint. I'd want to add strength to the repair by allowing it to be attached to the higher slab. There is even a nice little video by the manufacture about this: https://youtu.be/07blEEF0qxM
If you want to pour a larger more gentle transition on the low slab, then I'd add a true separation between the repair slabette (not a masonry term so don't use it around masons or you will be laughed at) and the higher slab. That way, if the slabs are continuing to move, it doesn't immediately wreck the repair job. I like the idea of using redwood or something relatively moisture impermeable. You can read more about gap filling here:
You might also want to add some acrylic concrete fortifier to the mix for added strength. Double check to make sure it is compatible with T&B though. If memory serves, it is.
Your height variation between slabs is rather substantial compared to the repair shown in the video. I encourage you to make the transition as gradual as possible. My friends in wheelchairs and old folks will be thankful for your efforts, as it is easy for we able-bodied folks to not be aware of how such things can make life miserable for them.