A root for “centre, middle”, it first appeared in The Etymologies of the 1930s as ᴹ√NED with augmented form ᴹ√ENED (Ety/ÉNED, NÉD). The only derivative of its unaugmented form was the Noldorin prefix N. nedh- “mid-”; its usual forms N. enedh/ᴹQ. ende were derived from the augmented form ᴹ√ENED. In notes from the 1950s and 60s, it seems this augmented form became the normal form, as in √EN(ED) “center, middle” (PE17/26) or ened- “middle” (VT47/26).
One complication in the later iterations of the root was the appearance of the word S. Enedwaith “Middle-region” in The Lord of the Rings maps and appendices (LotR/1089). I suspect this form dates from the period in Lord of the Rings drafts of the 1940s where Tolkien decided to represent [ð] as d: compare N. Fanuidol (TI/306) vs. S. Fanuidhol (LotR/283) and N. Galadrim (TI/239) vs. S. Galadhrim (LotR/341). For whatever reason, Enedwaith was never corrected, and in some places Tolkien said this was a mistake and the proper form should be Enedhwaith (PM/328; VT42/20) while in other places he considered revising the root for “middle” to √ENET or √HEN(ET) (VT41/16).
In his notes on numbers and fingers from 1968, Tolkien said the primitive form was ened with variant form enel (VT47/16, 29; VT48/9-10, 24-25), as the result of frequent d/l interchange in Common Eldarin (VT47/29). In these notes this “middle” root was likewise connected to √ENEK “three” as represented by the “middle” finger (VT48/10). In this set of 1968 notes Tolkien also said √ENET was connected to the distinct root √EN “again” and had the sense “one more” (VT47/15; VT48/25). As for the enel “middle” variant, it seems it was used more in Nandorin (VT47/29), but was a factor in some Quenya words such as Q. enelmo “go-between, intervener, intermediary, mediator” (VT47/14).
Neo-Eldarin: For purposes of Neo-Eldarin, I think it is best to assume the root for “middle” was mainly √ENED, and that Tolkien’s flirtations with √(H)ENET “middle” was a transient idea. I think it is also worth retaining the unaugmented prefix nedh- “mid-” for Neo-Sindarin words, though originating from a lost original vowel rather than a lack of augmentation.
This root had a variety of senses in Tolkien’s writings, which may or may not be related. In The Etymologies of the 1930s, ᴹ√EN was glossed “yonder, over there” with the adverbial form ᴹQ. en “there, look yon (yonder)” (Ety/EN) and in this sense it was probably a later iteration of the early demonstrative root ᴱ√E “that by you”. This 1930s version of the root seems to be a “remote demonstrative” as opposed to ᴹ√TA “that” which seems to be a more ordinary demonstrative.
In notes from the late 1940s and early 1950s, Q. en was connected to the future (PE22/120, 131; PE23/97), and in Common Eldarin: Noun Structure from the early 1950s, Tolkien revised the gloss of primitive ✶en from “yonder” to “next, further, again” (PE21/70, note #4). In later notes Tolkien primarily emphasized the sense “again” with the glosses like “go on doing” in notes from the late 1950s or early 1960s (PE17/167), and the glosses “again, once more” in a couple of different documents written in 1968 (VT47/15; VT48/25), though in one of these it was given the form √HEN “again”, probably a transient idea (VT41/16). This new meaning for √EN reflects the use of the prefix Q. en- for repetition, such as in enquantuva “shall refill” in the Q. Namárië poem (LotR/377).
It is not clear whether √EN retained the sense “yonder” in Tolkien’s later conception of it. In the aforementioned note where it was glossed “go on doing”, one of its derivatives was Q. en(a) “still” as in Q. quetir en “they still say” (PE17/167), referring to the past rather than the future. On the other hand, in rough notes written around 1968, Tolkien said “en- ‘again’ as [in] enquantuva is prob[ably] [?] ‘further, beyond’ [?in respect of time influenced by ? only in] Q. enta, only with verbs. [?root] ēn” (VT41/16). The words in brackets were added by Carl Hostetter as editorial additions or to indicate unclear text in the original, but the relatively clear glosses “further, beyond” show that at least in that moment, something like the 1930s meaning “yonder” of this root may have remained valid.