Yes, and no doubt this issue is made notably misty and more complex due to posthumously published texts.
Well put as I expected
But I would emphasize 'on the face of it', as the word
Avari was not employed in the final form of any text in the Appendix F, and the distinction between West-Elves [Eldar] versus the East-elves is maintained...
... but who are the East-elves? Not that you said otherwise, but I think they don't have to be Avari according to the author-published description [nor do the Minyar have to be named the
Vanyar necessarily, on the Eldarin side of this coin]. They could be Telerin, they could be Avarin, they could be a mix of Teleri and Avari, as they are some grouping of Elves that are yet distinct from the West-elves -- those Elves who passed Over Sea plus only the Sindar.
And so what remains once the mist of all this posthumous complexity is blown away? To my mind: most of the Elves of Lorien and Mirkwod are East-elves, not Eldar, nor their languages Eldarin.
Which JRRT not only decided to publish in the 1950s, but if he was unhappy with this scenario, he yet didn't revise it given the chance in the 1960s.