For stock plan, company makes the distinction between RSU and PSU (performance - triggered by company metric). TT doesn't have a PSU category - should I call it RSU?

I think this is the right thing to do - if I select "Other", TT says it will treat the sale as a private (i.e., not stock plan) sale.  None of the other options make sense.  I guess my only concern is whether a PSU has a potentially different tax treatment from an RSU, and that TT doesn't know about it.

Somehow didn't see this on my first search, but found someone from a couple years ago agreeing with this opinion:

https://ttlc.intuit.com/community/investments-and-rental-properties/discussion/re-how-should-we-classify-performance-stock-unit-awards-in-stocks-mu[product key removed]-other-section/01/1315175/highlight/true#M46240

Also found a document at E*Trade talking about stock plans where they discuss RSUs and PSUs in the same category, with examples of identical treatment.  https://us.etrade.com/knowledge/library/stock-plans/understanding-restricted-performance-stock

For 2023, TT no longer has an "Other" selection. Why doesn't TT have a performance award selection - even as it is treated the same as an RSU?

This is confusing. 

I am also having to select RSU, even thought it is not, to ensure the right tax treatment, right?

Yes, by marking it as a RSU, it will receive the right tax treatment. You can also refer to the article posted above by waisaacs.