Equiped with nothing but wiktionary (wikt.), this is impossible to answer succinctly, and that might be because answering correctly is difficult. If the first few etymologies to try are sadly incomplete, we might assume the problem is contested.
Within wiktionary, the problem can be approached from different angles, that lead to inconsistent answers.
I start with a modern word, its given reconstructions, the evident predecessors and the linked cognates, one language after another. Then I will try to sketch a wanting reconstruction of the development from the bottom up.
a) German 3rd p. sg. f. [sie] "she" in wikt. links a backprojected West-Germanic "*si" ("she, it"), alternative "*si(j)u", promissing Proto-Germanic *si without further explanation; Old High German "siu" is given as evidence as well as cognates as there are Gothic "si", Old English "seo" ("that one (f.)"); no own entry for siu of OHG is indexed
German 3rd p. pl. [sie] "they" in wikt is giving no reconstruction, only OHG forms that are inflected for case--as there are f., m. and n. respectively: "sio", "sie", "siu", thus not coinciding in the feminine genus with the singular, for OHG, rather in the neutral singular.
c) English [she] links PGem "*hijo" ("this, this one" f.), that is *hiz (m.)--reflected in " Middle English sche, hye (“she”), from earlier scho, hyo, ȝho (“she”), a phonetic development of Old English hēo, hīo (“she”), ...", therefore the phonologic explanation is sought in "palatization", relation to seo ("that one") deemed unlikely; cognates for example are given with Scottish sche, scho, West-Frisian hju, English he, and more, to conclude, ultimately: "ȝho is the immediate parent form of Middle English scho and sche."
Already we can see the noted difference between these etymologies. The phonetic explanation for "she" is slightly irregular. I don't want to spell out what it would mean for the development of *hit (it). It requires shift of stress without apparent motivation ("change in stress upon hío resulting in hió, spelt ȝho", "ȝh = hȝ").
Note: The OE h is translitterated already with IPA /x/ [h], that is debatable notation suggesting a phonemic palatal which was however not realized? In an idealized Old English lect? Iotization from the i in OE hio might account for something, at least (cp. West-Frisian hja, North-Frisian jü). Problematicly PIE *yus, and *yos are not discounted, and it doesn't either account for Dutch. Maybe Dutch is intentionally not listed as cognate. However:
d) Dutch [zij] "she", "they" links *hiz, too, but also *iz.
e) Old Saxon [siu] "she", "they" likewise links *hiz, *iz, but:
This is confusing, let's take a step back.
that (masculine singular form)
- Þone rǣd ġerǣdde Wīdsīþ. ― Widsith gave that advice.
Pronoun sē m (demonstrative pronoun)
that, he (masculine singular form)
Þā ne sacaþ. ― They do not quarrel.
[…] Middle English: se, ze, sæ
Declension [sēo, þæt, …]
definite article: the "sē māno ― the moon"
demonstrative adjective: that, those -- "Hē gaf thē gift. ― He gave that gift")
Declension [se, that, siu, …]
The term Anglo-Saxon exists for a reason (dated when?).
The conclusion seems to suggest itself, that two or more different paradigms had become conflated into one by chance. But we cannot jump to the conclusion that *h spontaneously sibilified to s through palatization in all those languages, independently. Gothic si "she" as the earliest evidence weighs rather heavy, but cannot on its own explain the plural. *si "she" also exists in Celtic, by the way. Wiktionary suggests "she" came from an independent, sporadic, phonetic development--which is doubtful.
DWDS sees the differentiation as a late development, doesn't mention she, and the conclusion is a logical account that however depends on the textual development accurately reflecting the oral development:
Das Pers.pron. der 3. Person Sing. entwickelt in Analogie zum einfachen Demonstrativum (Nominativ Sing. Fem. ahd. asächs. thiu, Akkusativ Sing. Fem. ahd. asächs. thia) einen entsprechenden femininen Nominativ ahd. asächs. siu bzw. Akkusativ ahd. asächs. sia. Das dadurch mit den starken Adjektiven endungsgleiche Personalpronomen bildet daraufhin diesen folgende Pluralformen wie Nominativ und Akkusativ Mask. ahd. sie, asächs. sia, sea, Fem. ahd. sio, asächs. sia, sea, Neutr. ahd. siu, asächs. siu, sia, sea. Bereits im Ahd. werden die vollen Formen vereinfacht zu sī, sie und si, die auch im Mhd. gelten (mnd. sē, mnl. si), bis sich im Nhd. sie (nl. zij) an allen Stellen durchsetzt
(Wolfgang Pfeifer, Etymologisches Wörterbuch der deutschen Sprache, "sie", bold emphasis mine)
Translation of the relevant parts: 3rd p.sg. in analogy to fem. thiu, m. thia *in both OHG and OE siu, sia; thereupon follow the pluralia; OHG simplifies these, MHG likewise (MLG, MNL).
Consider just for fun whether it car drives fast might feel acceptable. I think it's funny because it's not acceptable--not currently anyhow. However, dialectal "them country boys", "they folks", or appellative/ you irresponsible idiot, referential "Why you little ...", etc. do exist. And this goes a lot further if taking so into account, e.g. Ger. So sachen, which I'd naively interpret as su[ch] things, "solche Dinge", whichever would be so'ne Sachen in my regiolect (Berlin-Brandenburg), and the singular could be seen synchronicly as contraction from so [ei]ne Sache (su[ch] a thing), but that's impossible in the plural, because no plural for the indef. art. ein- "a, an" exists. So, therefore, so Sachen it shall be. Also compare Bavarian so'a Schmarn. I have recently read that Bavarian "a" and English "a" are independent developments, although, those opinions have nothing to recommend themselves except the supposed distance. Bavarian is by the way far from Modern High German, but was once closer to High German-y (that is Germania Superior). Likewise, the loss of so as definite article is so far supposed to be have developed independently. Articles are expected to have developed relatively late from determiners and demonstratives (cf. *so, there, da). The details are not perfectly understood, because these too are found to be independent developments in the individual branches of Proto-Indo-European, so external comparison falls flat. The threepartite gender system likely followed a two-way distinction animate-inanimate, therefore the gloss *si "she, it" makes some sense, also that wife is neutre (like Old Irish be), or that some Hessen and Swabian dialects regularly use das Marie, but all that is poorly understood. Pfeifer succinctly devides both stems:
[...] Pronominalstamm ie. *te-, *to-, der auch in allen obliquen Kasus auftritt.
[besides] Nominativ Sing. Mask. und Fem. […] s- anlautenden Stamm (ie. *so m., *sā f., […]
(Wolfgang Pfeifer, Etymologisches Wörterbuch der deutschen Sprache, "das [pron.]")
I had initially promissed to now derive these pronouns from first principles. At that I had hoped to rest my argument on the further reconstructions, as there are quite interesting roots. But this is impossible to achieve from the above notes alone.
PS: Save to say, they is described as a loan from Norse. This is comparable to Ger die, not Sie.