Shaykh Muqbil rahimahullah advises those who hold the Mushaf in their hands during Taraweeh prayer in order to follow the Imam in his recitation that they should leave this action off and that it is something makrooh.
Ash-Shaykh Albany, rahimahullah, mentioned that carrying the Mushaf in the salaat leads to the person making a number of unnecessary movements in the salaat, for example putting the Mushaf in his pocket and taking it back out from his pocket, and as well opening and closing the Mushaf along with turning the pages when following the Imam. Likewise, the Shaykh rahimahullah mentioned that at times the person who is holding the Mushaf in his hands may have to place the Mushaf under his armpits, especially when he intends to raise his hands or to do ruku or sujood, and as a result, he displays his hands as if he is tied to something.
Using the Quran app while following the Imam in the salaat comes with more complications.
AbdulFattaah Bin Uthman