I agree with your first statement, but I’m not sure I understand what you’re saying here:

> there’s really no first principles reason for any legitimacy

Do you mean in this case, or are you making a blanket statement about the nature of morality and power?

I'd rather talk about whether the protests were "genuine" rather than "legitimate". Riots usually escalate from prior peaceful protests, in which protestors claim specific concerns and political factions get involved. None of that seems to have happened here, it was zero to teens rioting.

Yes, there are. A popular protest (and even riots!) should come entirely or at least in the vast majority from a sentiment spread across the people. If it's 500 youngsters that come out of the blue following a campaign orchestrated most probably by a foreign state actor, then it's not legitimate.

Yes, we could start doing verbal and mental gymnastics about how an external actor could be legitimately interested to try and drive the political landscape of a country one month before elections, sure. But it's not the point here.