Should an independent contractor include unemployment payments received in 2020 (1099G-PUA pymts.) as "business income", like with a 1099MISC/NEC,

No. Unemployment income is not reported on Sch C. Report it separately as 1099-G. 

Many Thanks - and to confirm, even if payments were received under the independent contractor/pandemic benefits package it is still considered "personal" income vs. "business" income?

Correct. Which is good news since if you reported it as business income you would have to pay self employment tax on it. 

Many thanks!