The earliest iteration of this root was ᴱ√ROTO “hollow” from the Qenya Lexicon of the 1910s, with derivatives like ᴱQ. rotl “cave, hollow” and ᴱQ. rotse “pipe, tube” (QL/80). The primitive root ᴱ√roto also appeared in the contemporaneous Gnomish Lexicon with derivatives like G. rod “tube, stem” and G. †roth “cave, grot” (GL/65). The root reappeared as ᴹ√ROT “bore, tunnel” as a late addition to The Etymologies of the 1930s that Christopher Tolkien omitted from the published version of The Lost Road; it had with derivatives ᴹQ. rotto/N. (g)roth “cave, tunnel” (EtyAC/ROT), and was also an element in the name N. Nogrod (EtyAC/NAUK).
The root appeared as √ROT “cave” in notes on Words, Phrases and Passages in the Lord of the Rings from the late 1950s or early 1960s (PE17/49), as ✱groto “dig, excavate, tunnel” in the Quendi and Eldar essay of 1959-60 (WJ/414), as unglossed (g)roto in other notes associated with that document (VT39/9) and as rot, s-rot “delve underground, excavate, tunnel” in notes associated with The Shibboleth of Fëanor from 1968 (PM/365 note #56). Thus in later writings the root √ROT had variants √GROT and √SROT.
Neo-Eldarin: For purposes of Neo-Eldarin I would ignore the gloss “cave” which seems to be a loose translation, and stick with the meaning “excavate, tunnel, bore” for the root √ROT; I’d also retain the meaning “hollow” from the 1910s to allow salvaging similar early words from the Qenya and Gnomish Lexicon.
Roots with an s-prefix were common in Elvish throughout Tolkien’s life. In notes from around 1967 discussing the root √SKAL, Tolkien considered giving the s-prefix a more specific sense:
> Keep this part so far as it affects SKAL [“cover, veil, cloak, conceal”]. SKAL & KHAL were both probably primitively related, being differentiated from a √KAL, made to distinguish this from KAL which became applied to “light”. s- was primarily “privative” [in] meaning. Cf. √STIN-, grey, compared with √TIN-, sparkling; √SKOR-, rough, marred, unequal or unsymmetrical in shape, to KOR, round (PE17/184).
As interesting as this is, Tolkien mentioned this function nowhere else, and there are plenty of s-prefixed roots that have nothing to do with privation. Furthermore, while √SKAL is mentioned several times in Tolkien’s writings, √SKOR “unsymmetrical” appears nowhere else, and the usual root for “grey” is √THIN, not √STIN.