Why is the Proto-Sino-Tibetan word for "eight" reconstructed as "triat", when in nearly all Sino-Tibetan languages it begins with either 'p' or 'b'?
There has never been an attempt in reconstructing Proto-Sino-Tibetan (PST, Chin. 漢藏語) for eight. What is shown in the link is perhaps a mislabel for another reconstruction, or an unreferenced, dubious attempt in PST reconstruction.

There were only five referenced Proto-Tibeto-Burman (PTB, Chin. 藏緬語) reconstructions. PTB for eight is *b-r-gyat ⪤ *b-g-ryat. They are recognised as cognates.

The difference between PTB and PST is that Sinitic languages are excluded in the reconstruction of PTB. That does not mean, however, that there is no comparability between PTB and Chinese, as shown below.

From Wiktionary: 'This is a doubly prefixed root, justified mainly by Written Tibetan, Jingpho and Rgyalrong forms. As expected, this root was particularly prone to metathesis and preemption. The Chinese form, for example, shows preemption of the rest of the initial cluster by the labial prefix, resulting in a *pr- &gt; p- initial.' (As in pˤret &gt; peat from Old to Middle Chinese.)