Mulberry can do a very good wine if you doctor the acid flavors,

it can be a nothing if you run it with only a pH correction using acid blend,
To your question about stems, I haven’t had a flavor issue with green material, I currently juice them before fermenting, a decade ago I probably did a whole berry ferment ,,, HOWEVER I have had a light mold flavor when using the sheet on the ground to rake berries out of the tree, ,,, a guess is that old shrunken/ dried fruit gave the flavor.
This years pick came in at pH 4.68; TA 0.65%; gravity 1.050; Last years pH 4.36; TA 0.54; gravity 1.041; The sugars and acid change a lot in the day where it changes to dark purple so you are compromising fruitiness vs enough acid. It is hard to push the pH of mulberry juice to the low 3’s
The recipe
mulberry juice . . . 3.n kg
lemon juice . . . . . 0.5 kg
sugar . . . . . . . . . . 0.6 kg
acid blend . . . . . . 20 gm
yeast nutrient
K meta
water . . . . . NONE
A last note, to get rid of the pigment on your fingers or nylon bag, ,,,, it is easily decolorized with acid,, I ”bleach” with vinegar to get stuff white again.