Sram Eagle NX Rear Derailleur not reacting to cable tension
If you've replaced the cabling and you see it slackening off with no derailleur response, there must be some added resistance in the movement of the derailleur itself.
I suspect it is simply the pivots of the derailleur which need some lubrication. Either a spray of teflon lube on each pivot point or a drop of oil. Then, if you have the wheel off the ground, you can move the derailleur up and down the cassette while spinning the pedals, to exercise the pivots and free them up. Just mind your fingers.
Double check the guide pulley is far enough away from the cogs, something like 13mm from the largest cog for Eagle, so a decent gap.
I can't think what else would resist the return force of the derailleur spring, except a lack of spring tension... if you handle the mech and it still has finger-crushing spring tension then all good, but check the spring for any defects.