The reconstructed root of one is not present in the Anatolian and Tocharian branches of Indo-European. It will be helpful to illustrate this in more detail:
- Tocharian B (Adams 2013) ṣe: "one", "same", "some", "together";
... directly equatable with Greek
heîs (< PIE *sm-s or possibly *sem-s). More distantly we have Armenian mi
(reflecting *sm-ihxos) ‘one,’ Gothic sin-teins ‘daily,’ Old English sinnihte ‘eternal night,’ Latin sem-per ‘always,’ etc. (P:902-904; MA:399). This connection goes
back to Sieg/Siegling, 1908:927, and Meillet, 1911-12:284-5.
This Old English sinnihte is similar to the construction of fortnight "2 weeks; 14 nights" and sennight, OE seofeniht "1 week". The meaning "eternal" is also present in Thocharian B ṣek "always". Adams argues that, "The semantic development is ‘once for all’ to ‘always’ and one should compare, mutatis mutandis, Latin sem-per (Meillet and Lévi, 1911:451; cf. MA:410). Otherwise VW:453-454 (from *sgh-) […]
Adams admits many more derivations, especially ṣemeske "only, sole; private" may be of note. This seems to match the first part of the question, some dozen, approximately. "up to" is collocated in the phrase […] śak täṅte.
Problematically, however, the initial of Toch. B śak "ten" < *déḱm̥- "is difficult, since we might ordinarily expect either ts- or c-" (Adams)—cp. Toch. śak-śe "eleven", śak-wi ‘twelve’, śkänte-wäte "twelfth" etc. and English dozen (en.WT): Old French douzaine, doze + -aine, from Lat. douodecim; -aine "(noun) indicates approximation, suffixed to a number". Wartburg (FEW: duodecim) refers to [A Gl. 9, 60 n. 4] (sigel resolved in Beiheft, not available to me rn) for the suffix, though separating Old Provencal dotzen from dozen – right to tax, of wine etc. (translation mine) makes it similar to tithe "tenth" and to Tocharian B śkanno "tithe", as **śkanto is derivable as feminine from śkante "tenth" (Adams)—a gloss of Sanskrit daśamá "tenth", from *déḱm̥-.
Discussion of possible relations between **déḱm̥- "10", **ḱm̥t- "100" and *sem- vel sim. in (Eskes 2020) does not account for *dḱ > *s or *só / *to &c. as far as I can tell. Their notion of conditioned **d > **h1 (Kortlandt Effect) should at least be relatable to the root of one < **h1oy-nos, which leaves a lot to be explained.
- Hittite (Kloekhorst, 2008): ši- (numeral) "one"; šani (adj.) "the same, one and the same"
The Anaotlian numerals are difficult because they are almost always written logographically. Kloekhorst reconstructs *sih2- "one" without further etymology. He notes formal problems for a derivation of šani from *sem (pace Eichner). However, he provisionally eccepted *som- in another lemma:
sentence particle indicating superposition (‘over’ , ‘upon’ , ‘on’ etc.);
indicating contiguity or close proximity; accompanying ‘for (the benefit of)’ or
‘about, concerning’ ; accompanying ideas of measuring or counting; indicating ‘of, from’ (only OH).
The list of ultimately uncertain, superficially similar lemmas is of course too long to brood force our way through.
In addition, both Tocharian and Hittite admit borrowing from Indo-Iranian. E.g. Toch B śkä-maiyya – of ten powers – in loan translation to Prakrit daśabala, an epithet of Buddha.
Eventually, nothing much on the collective sense of assemble turned up in my search, as German adv. insgesamt "in sum, total, all told" would suggest, though it should fit the opening question's second example, "[sum] seven speakers preceded me, so no one listened to my speech." Toch. B ṣäms "count" is close enough, cp. (Adams) Sanskrit samayati "puts in order", Old Norse semja "put together, put in order, unite", Toch. B ṣämla- "count" also in collocation: "countless".
someone comes possibly from rebracketing so many - *some any. Point in case, German so manche is formally equivalent to so many, but it patently means some, a couple, any; also manch einer "some people" is formally equivalent to the "many a" construction, e.g. manchenorts "many a place" (cf. collinsdictionary german-english: manch). It could be the other way around or complete coincidence. The fact is that it works.
This pertains to the second part of the question, exactly:
Some speakers preceded me, so no one listened to my speech.
[So many] speakers preceded me, so no one listened to my speech.
He had some jellybeans and threw up.
He had [so many] jellybeans [he] threw up.
The latter is an example of stranding, I believe. The former is remarkable for the repeated so.
Further relations to the Old English indefinite pronoun man "one", German man, jemand "somebody", jederman "anybody" are obscure.