Skeleton Spawner - How far do you need to move skeletons to spawn more?

After Minecraft wiki:

If, at the time of spawning, 6 or more mobs of the spawner's type are present within a 9×9×9 area centered on the spawner block (in Java Edition) or a 16×10×16 area centered on the lower northeast corner of the spawner block (in Bedrock Edition), the spawner "poofs" without creating any mobs and then waits for the next cycle.

This is not the problem you're facing though. What you're facing is known as entity cramming - a limit of 24 mobs per block of space. This has nothing to do with the spawners or distances, it's just too many mobs (any!) in too small space.

In Java Edition, entities will take damage if too many are packed into the same space. Specifically, the maxEntityCramming gamerule defines the maximum number, above which a player or mob takes [3 hp] suffocation damage every half-second, as long as that player or mob is pushing greater than that number of other entities. Pushable entities include players, mobs, boats and minecarts.

The easiest solution is placing a ladder or vines in the space the skeletons occupy - these disable entity cramming damage within their blocks.