Any tips on muting technique? Maybe about the dynamics of the fretting hand and the picking hand muting
You are going to get a lot of different answers and opinions on this, and that’s because there isn’t one perfect answer; at least one that will work for everyone in every situation for every occasion.
I think the first part is identifying where you think most of the unacceptable noise is originating. From there you can kind of methodically tackle it.
At least in terms of the picking hand, there’s no easy answer because it depends on what your picking hand technique is.
Someone who uses non-anchored rotational picking a la Django basically doesn’t do much right hand muting, for example, while someone who uses an anchored deviation picking style probably has the meat of their palm on or close to the strings at all times.
Figure out what picking style you have and then we can give more concrete answers.