Just to make it clear:
The prayer is an independent kind of worship which in fact combines the 4 other pillars of islam! A part of a prayer as the Messenger of Allah (peace be upon him) taught as is reciting the fatiha and some verses of the Quran while standing! Therefore praying Taraweh or any other prayer as we do is perfectly permissible and sunna (if not even fard/farz for those who can stand!)!
Now is it' permissible to read/recite Quran while standing?
Well yes it's not common if we exclude the daily prayers. And standing and reading Quran is neither convenient nor very helpful to concentrate on this kind of worship (if it's not during a prayer).
But Allah (Ta'ala) says in the Quran:
- Who remember Allah while standing or sitting or [lying] on their sides and give thought to the creation of the heavens and the
earth, [saying], "Our Lord, You did not create this aimlessly; exalted
are You [above such a thing]; then protect us from the punishment of
[Surat al-I'mran (2:191)]
- And when you have completed the prayer, remember Allah standing, sitting, or [lying] on your sides. But when you become secure,
re-establish [regular] prayer. Indeed, prayer has been decreed upon
the believers a decree of specified times.
[Surat an-Nisa' (4:103)]
remember Allah: is dhikr Allah this mean's dua', dhikr/tasbih/tahlil/takbir/ and of course also reciting Quran!
This mean's we can read Quran in any position as long as we do it as it should with the right concentration...
as an Addition here a Fatwa (Arabic)
And Allah knows best!