The light speed limitation only restricts anything that can transmit information from one place to another, such as you could do with light (e.g. radio waves).
If you aimed a laser pointer at a very distant screen, and then panned it across from point A to point B, the spot of light on the screen could conceivably appear to be going from point A to point B faster than the speed of light, but it can’t carry any information from point A to point B, so it’s not an issue for relativity.
Nothing is actually moving from one end of the universe to the other as a result of the expansion of space, so it’s not a situation that invokes relativity. Like the laser pointer, it’s just you looking at both moving points and ascribing some meaning to them
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