That's not clear. I took my
~/Library/Application Support/Sublime Text 3/ out to Desktop, copied the names of
Installed Packaged and carefully installed over the pristine ST3 everything, watching after each package if there appear the ghost second ST3 icon. I installed everything and nothing appeared, so, the problem was not in the installed packaged but in something executing ST again… funnily not in a recursive way. After installed all the packages I needed to move my previous (dense)
Installed Package/User directory. No problems now. Very strange.