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You can add Muffled as a mod to leg armor. It says that it "Reduces detection from moving".
The 4th level of the Agility-based Sneak perk says that "running no longer adversely affects stealth".
Since "running" is the most extreme form of movement, if it doesn't affect stealth, then that implies that no movement at all will affect stealth. Does this mean that Muffled no longer has an effect once you get the 4th level of Sneak?
If so, I can replace all my Muffled mods now that I have this perk.
No, since sneak walking will still incur a penalty.
I'm re-using my answer from Fallout: New Vegas due to the game using a very similar system.
There are four modes of movement:
Run, Walk, Sneak Run, Sneak Walk.
Most people don't know about Sneak Walk, but it is the slowest speed. If you are sneaking and can catch up to a walking person, you are doing Sneak Running.
You are more easily detected when Sneak Running than Sneak Walking. The perk allows you to Sneak Run without being more easily detected.
However, Sneak Walking is still easier to detect than sneak without moving, so Muffled mods will still have a use.
While the Sneak perk removes the stealth penalty from running, there is still a penalty for movement. With the perk, you have the same penalty for running as you do walking, but there's still a penalty and the Muffled mod will reduce that penalty as well.
This is how Sneak functioned in previous games and there's no reason to believe that it functions any differently.
Yes, they are redundant.
Although the description for Sneak Lvl 4 does not say how running previously affected stealth, and therefore what exactly it changes, it probably works the same way as the Silent Running perk from previous Fallout games. Nukapedia agrees with this assessment. Looking at the Silent Running page, we read that
Fallout 4: The effects of this perk are found in the rank 4 of the Sneak perk.
That page also describes the effects of the Silent Running perk, saying that
Silent Running completely negates ALL movement penalties, regardless of movement speed. The detection level for the player character is the same, when standing still or moving around, no matter if moving slowly or running around.
Therefore, there are no "penalties due to movement" for Muffled to reduce.
Update from Experience
I've now experienced days of playtime with characters who have Sneak Lvl 4.
The only time my movement while crouched seems to cause enemies to detect me is when it changes how much of me they can see (like going around a corner, moving through bushes, or stepping into the light), when they can see me and I move closer to them, or when I knock something over and it makes noise.
