Ok back to it :
Beckwith book was published in 1987 . To my knowledge it is the only book on the history of the Tibetan Empire in Central Asia. Beckwith could analyse some "recent works" which I could not find and he had the advantage of reading original historical textes . So I hope he is mostly right.
Pg 88 of his book is about the TURGIS alliance and mention an alliance in 717 ( august ). He tells us that Chinese and Arabic sources, both mention an assault by a "turgis led allied army of Tibetans, Arabs and Turgi " which led siege to Aksu and Ur-Turfan.
The Tand did sent an army composed of ethnic turks that drove off the allies.
The footnote (22) mention also as source TCTC 211:6728 or Ssu-ma Kuang, Tzu Chih t'ung chien, 10 vols, peking 1956, repr Taïpeï 1979 ( sorry I do not read Chinese and could not find any translation )
The information adds the footnote is also contained in a memorial to the throne by T'ang Chia-hui
We know that after defeat, the arabs did flee back to their own territory.
We also know that " at the same time"A Tibetan army was severely defeated ( so A different army or the allied contingent is not know )
A 2016 paper published by Wiley Blackwell on the Tukulor empire very briefly mention the 717 alliance with Tibet but does not mention the arabs. The campaign is very briefly described as they led siege and were defeated
The following link just stipulates that in 717 a combined army as described in this post and led by Suluk was indeed defeated in 717 ( but the source is Beckwith )
https://www.wikizero.org/wiki/en/Timeline_of_the_T%C3%BCrgeshWork on that historical period and subject are very very uncommon and arab / Chinese sources are a complete mystery to me
Now up to you