Salat at’tasabeeh is not an authentic prayer and one shouldn’t perform it. know of what Sheikh Al Albanni has said and of his authentication of the hadeeth.
The hadeeth was graded weak and not authentic by a number of other scholars such as Ibn Al Jawzi, Ibn Taimiyah, Ibn Al Qay’yim, Ibn Bazz and Ibn Othaimeen among many others.
The reason of their weakening the hadeeth is a number of things. Among them the strange description of this prayer. As it includes saying thikr after finishing the recitation of the Quran while in the standing position. No other prayer has this in it like this.
If this was a good thing to do, the Prophet salla Allahu wa sallam would encourage people to do it. In the hadeeth, it states that if you do it once in a life time as if you do it every single day.
This great prayer, if it was authentic, it would have been famous and well known among the companions of the Prophet salla Allahu alaihi wa sallam. We find that no one knew about it except at the time of the followers of the companions, may Allah be pleased with them. Even then, it was still not famous or practiced which indicates that it wasn’t authentic.