When an object approaches the speed of light, it does not necessarily mean that it moves more in the fabric of spacetime. In fact, it's the opposite: as an object's velocity approaches the speed of light, its motion through space is increasingly limited, and its motion through time becomes relatively slower. This effect is known as time dilation.
According to the theory of relativity, the speed of light is a fundamental constant that is the same for all observers, regardless of their relative motion. As an object accelerates and approaches the speed of light, its energy and momentum increase significantly, and so does the curvature of its path through spacetime.
As an object moves faster, its "proper time," which is the time experienced by the object itself, is dilated or stretched relative to an observer in a different frame of reference. This means that from the perspective of an observer in a stationary frame, time appears to pass more slowly for the object in motion.
From the perspective of the object in motion, however, it experiences time normally. It's the external observer who perceives the passage of time for the moving object to be slower.
The reason for this apparent contradiction is that space and time are interconnected in the fabric of spacetime. As an object's velocity approaches the speed of light, its motion through space is constrained, which leads to time dilation. In other words, the more an object moves through space (closer to the speed of light), the less it moves through time relative to an observer in a different frame of reference.