This root was connected to bread and baking for all of Tolkien’s life. It first appeared as ᴱ√M(B)ASA “cook, bake” in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. maksa- “cook” and ᴱQ. masta “bread” (QL/59). In this period, both unstrengthened and strengthened forms were used as indicated by the Gnomish roots bas or mas (QL/59), both reflected by words in the contemporaneous Gnomish Lexicon like G. bast “bread”, G. brath- “to cook”, and G. mast “feed, food, nourishment; fodder” (GL/22, 24, 56), though the mas- words seem to be influenced by ᴱ√MATA “eat”.
The root appeared as ᴹ√MBAS in The Etymologies of the 1930s with the derivatives like ᴹQ. masta/N. bast “bread” and ᴹQ. masta- “bake” (Ety/MBAS). When this root was first written it had the gloss “knead” and an unstrengthened form ᴹ√MAS, but both of these were crossed through (EtyAC/MBAS). The sense “knead” was transferred to the root ᴹ√MASAG, which still shows signs of unstrengthened ᴹ√MAS (Ety/MASAG). The root √MBAS “bake” appeared again in notes from the 1960s discussing the origin of S. lembas (PE17/51).
This root was connected to the sense “dwell” for all of Tolkien’s life. In the Qenya Lexicon of the 1910s it appeared as ᴱ√MBARA “dwell, live”, though in Qenya it was blended with ᴱ√ŊWAÐA “tarry, linger” since [[eq|initial [ŋʷ] became [m]]] (QL/60). In Gnomish the two roots remained distinct: G. bar “home” (GL/21) vs. G. gwadh- “dwell” (GL/46). However, other Gnomish derivatives hint at an unstrengthened variant ᴱ√MARA: G. mar “Earth, ground, soil” and G. Môr “The Earth”, of which Tolkien said “mar and môr probably conceal two roots and a confusion; mbara” (GL/56). The source of this confusion might be ᴱ√MARA “ripe” (QL/59, 63).
In The Etymologies of the 1930s the root appeared as ᴹ√MBAR “dwell, inhabit” (Ety/MBAR); an earlier version of this entry had the extra gloss “build” (EtyAC/MBAR). In The Etymologies, it seems this root was a strengthened form of ᴹ√BAR “raise” (Ety/BAR), but the root ᴹ√MBARAT “fate” seems to be unrelated at this point (Ety/MBARAT). The root mbar- was mentioned in the Outline of Phonetic Development (OP1) from the 1940s (PE19/36) and again as √MBAR “{house >>} dwell” in the second version of Tengwesta Qenderinwa (TQ2) from around 1950 (PE18/92).
The root √MBAR still had the basic sense “dwell” in Notes on Galadriel’s Song (NGS) from the late 1950s or early 1960s (PE17/64); in those notes it seems it was distinct from both √BAR “raise” and √MAR(AT) or √MBART “doom, fate” (PE17/66). But in notes on Fate from 1968 (NM/226-231; PE17/104-109), Tolkien shifted the meaning of the root:
> English “settle” in its various branches of meaning closely resembles the development of the meanings of √MBAR: thus settlement can mean the act of colonizing or taking up an abode, or the area or place so occupied (by a family or community); or (the terms of) an agreement fixed after debate. The development was not, however, the same: the senses of settle proceed from a sense “place in or take up” a firm position, especially in a place that seems suitable; from which the sense of settling affairs that were in confusion or doubt arose. √MBAR meant basically to make a decision, and the meanings relating to dwelling or occupying land proceeded from that (PE17/105).
This new definition for √MBAR was to support a more direct connection between this root and words like Q. umbar “fate”, hence establishing an etymological relationship to extended √MBARAT for the first time, for example with √MBAR > ✶mbartā- “to define, decree, destine” (PE17/104).
Neo-Eldarin: For purposes of Neo-Eldarin, I think this late 1960s meaning “settle, decide, establish; (by extension) dwell” is probably the best.