But what is might here?

Historically, "might" correlated near perfectly with "population size". From Sumer onward, the size of your army & slave count determined right-making (in the UN sense). Exceptions due to technology innovations were sparse and short-lived.

Therefore subsequent evolution has been mostly around how to manage large groups of humans, through "social contracts" and various domestication measures. The social configurations that managed better, won over those that did worse.

In other words, huge centralized states have been a huge evolutionary success. There are pretty much no independent ("sovereign" when it comes to right-making, UN or otherwise) small groups of humans any more, they got all gobbled up by superstates.

But I wonder if our institutions have fully caught up to the fact that the number of humans is near-irrelevant now. With the right technology, a small group can dominate millions, billions. And their necessary supply chain is tiny, relative to the purported UN jurisdiction – by a factor of at least 1000x.

So "democracy as right making" is at DIRECT ODDS with "might as right making". I wonder how this clash between where the power resides (technology and its homeostatic supply chain) and where people think it resides (themselves and their divine individuality) will play out. The emperor has no clothes.

If you are correct and it's all down to majorities bullying minorities around, how can we motivate human rights? Especially since they seem to have been instituted to prevent majorities bullying minorities around.

Reduce power of the majority by collectively limiting power of government.

That's exactly what having basic rights and human rights does.

Of course this is a bit circular reasoning because this works only if everyone abides by these rules, so in practice protects only against relatively 'mild' infringements and situations (i.e. the people are expected to be reasonable enough not to vote extremists in power... if not, all bets are off but that's true of all laws)

Don't blame the player, blame the game. Democracy will always converge into extremism the more power government has over people's lives. If you become reliant on government acting violently against the power minority and let government increase it's power, it will always lead to this.

It's self feeding problem. The only solution is slowly to deny government power over people.

And what happens when government stops being the majority power in a country? Should we still work to limit the power of government, or should we work towards limiting the power of the new majority?

The issue is whether the new majority power gives itself monopoly of violence.