After every four rakaats of Taraweeh, a short pause is taken by the Imam and the Muqtadis (followers). The purpose of this ‘pause’ is to take a short rest between the rakaats of Taraweeh. During this ‘break’, one has the option of remaining silent, (reciting Tasbeeh) glorifying Allah, praising Allah, reciting Quran or performing Nafl Salaah individually. A person has the choice of doing any of the above on an individual basis, without making it essential upon others, and without doing an act in a manner that it disturbs another person (in doing what he wants to do).
With respect to the ‘Tasbeeh’ that is recited in different mosques, these are indeed sacred words of glorification to Allah, however, it cannot be made binding upon everyone. Similarly, it is not proper to recite it collectively in a loud tone, since in this manner, others can be affected in doing whatever they wish to do on an individual basis. Besides this, the recitation of the Tasbeeh on a collective basis has never been practiced by the Sahabahs, Tabieen and the generations after them. Tasbeeh, etc. are all allowed, however, this will be on an individual basis.
Since the words of the Tasbeeh are great words through which Allah is glorified, it is permissible for one to recite it during the break in Taraweeh prayer. However, it must be done on an individual basis and not collectively. One must not believe that reciting this Tasbeeh is part of the Amaal (practices) of Taraweeh Salah, and one must not believe that these are duas of the Prophet ﷺ. If one wishes, he can recite it on an individual basis and he can also remain silent and rest. One who does not recite it, must not blamed or accused of having done something wrong.