Why is there no horizontal buoyant force?
The origin of buoyant force is earth’s gravitational pull, which is basically “vertical” at a point on the earth’s surface. You don’t possibly have another object to the side, so heavy that it can affect earth’s gravitational pull. Buoyancy is the reaction force to explain why an object, which has a finite weight, is floating in water. In deep space where gravity is extremely weak, the object will not experience much buoyancy at all (in deep space, up or down has no meaning either).