So, to my knowledge, here is how this went.

They took the disproven wolf analogy literally and resulted in Alphas and Betas.

Alphas are basically confident, attractive, and charismatic. Alphas get and say what they want.

Betas basically lack at least 2 of these attributes. Betas were also initially 'nice guys' before that term got memed into oblivion, ie, they would be negotiable, willing to accept compromise.

Basically Alphas are bad boy / jocks and Betas are shy but polite nerds.

And for a while this permeated.

At some point, the communities using these terms more or less realized they were nearly all, in actuality, Betas.

Then, Gamma Delta and Omega all came about in roughly the same time, and the system was reworked.

Alpha: Confident Successful Leader

Beta: Cooperative Loyal Subservient

Gamma: More Confident than Alphas, but doesn't care to lead groups, therefore is aloof / adventurous.

Delta: Basically 'Enlightened Loner'. Someone who isn't interested in much socializing and has little or no outward personal connections. (Basically a nice way of framing being a NEET or hikikomori, a cope)

Omega: Someone who is so above all this nonsense they don't give a fuck, because they are so smart and successful without anyone's help.

Next we got Sigmas: Somehow even more OP than Omegas, Sigma males are intelligent, capable of manipulating any social hierarchy to their own ends, capable of doing basically anything but they are so cool they just do that shit when they feel like it and then vanish when bored. Almost every video about a Sigma Male will show John Wick.

As you say, sigmas came about within around 6 months of the term incel and incel communities / identity becoming decently established in internet culture. So yeah, this is an even harder cope than Deltas, as theyre now all acting like they could absolutely do x if I wanted to, I just don't feel like it.

Finally we now apparently have Zetas.

Zetas are apparently somehow even more OP than Sigmas, being a kind of hybrid of Alphas and Sigmas. Its something like... I am a highly conventionally successful person and am very skilled and talented and clever but whoo boy do I get tired of social interactions some times.

(In reality, this is basically anyone who has held down a decent job for a few years and is quite egotistical, but not constantly assertive or boastful).

Zetas are fairly new and still being actively reworked.

I think the idea of a Zeta Male can best be explained by the number of previously but no longer successful tech bros being laid off or fired ot divorced recently.

So basically its TechLead and people like him doing fanfiction of themselves.

So... Alphas, Betas and Zetas are very social. Deltas are not, Sigmas and Gammas are social occasionally and Omegas hate socializing but do it anyway.

Basically this shit reads like someone who has only watched action movies attempting to develop character archetypes, and that is largely because so much of this just is directly based off of action movies from the 80s onward and boys and men trying to find their favorite analogues.