Water – Mix a bag of 25KG self-leveling concrete with 6L of water

From the description and photograph, it appears that the crack is the natural result of the sort of stresses one would expect at a location with:

• Drastic change in slab width to extend the slab through the door opening.

• Drastic change in thermal stress where the slab transitions from interior temperatures to exterior temperatures.

• Drastic change in slab stiffness. Dynamic vehicle loads are applied sequentially from the rigidly supported portion directly above the wall below to the spanning portion where they create deflection in the supporting structure.

All of which is to say that repairing the joint does not mean filling it in. There will always be a joint there. Instead, repairing the joint probably consists of keeping water out using backer rod and a flexible traffic sealant rated for wide joints...and perhaps a metal joint cover.

There's no magic in a can that it going to defy the laws of physics or change the internal stresses of a concrete slab under dynamic vehicular loads. Any repair needs to be premised on acceptance that there will be a joint across the opening where the slab narrows.

I'd remove the vinyl. The leveling compound should go on top of the bare concrete.
But before you do anything: check if the foundations are okay. If the floor isn't properly supported, the added weight from the leveling compound will make the floor subside faster.