Considered Eldar? Perhaps, not by you. I believe as you say that the Eldar are those who went on the Great March. The First Sundering, determined who was Eldar and who was Avari, and it seems the Avari never enter into the Books afterwards at all, except via oblique references such as being the early helpers of the Secondborn.
In contrast, the Silvan Elves are of the Telerin branch of the Eldar, split-off at the Second Sundering, and thus Eldar (albeit barely) but with the right and inclination (for the most part) to eventually depart into the West as attempted by Amroth and Nimrodel, and likely successfully done eventually in the Second, Third and Fourth Ages my most of their kind.
To wit, I offer the following from the Unfinished Tales, which is a quote of Tolkien from a late 'etymological discussion' in Appendix A of the History of Galadriel and Celeborn:
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The Silvan Elves (Tawarwaith) were in origin Teleri, and so remoter kin of the Sindar, though even longer separated from them than the Teleri of Valinor. They were descended from those of the Teleri who, on the Great Journey, were daunted by the Misty Mountains and lingered in the Vale of Anduin, and so never reach Beleriand or the Sea. They were thus closer akin to the Nandor (otherwise called the Green-elves) of Ossiriand, who eventually crossed the moutains and came at last into Beleriand
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