Is there any legal basis for a hadith that describes a supererogatory prayer of two rak'ahs, in which Surat Al-Ikhlas is recited seven times after Al-Fatiha in each rak'ah, followed by seeking forgiveness seventy times without speaking, and it is claimed that it erases sins, and is attributed to Ibn Abbas?

There is no basis for a specific Sunnah (definition) prayer during Qiyam (definition) al-Layl that involves reciting Surat al-Ikhlas (definition) seven times, as acts of worship are prescriptive. Specifying a particular remembrance, such as seeking forgiveness seventy times between the rak'ahs of Tarawih, is an innovation (bid'ah). One should avoid collective dhikr and raising the voice with it after every two salutations in Tarawih, due to the innovation involved therein.