If we are heading towards Tyranny or towards period of emancipation depends purely on the framework in which human society continues to operate.
It looks like that Internet-based informal Economy that can not be controlled by any national government will become ever only more prevalent which can gradually lead to extinction of all overreaching authorities denying tools necessary to implement effective Tyranny.
If Anarchy would be the final outcome than world would be nothing as we could currently imagine or as Plato ever could. Assuming Humanity would be granted 100 percent unemployment through support of AI based robots there is really no reason to fear such outcome.
Still, whether you like government, authority or not, these systems, more so on authority was put in place because there were desires for more safe, less criminal envoirments. If these figures with a role of authority completely lose their grip on the power they currently possess then we would be in a state of anarchy, considering all the violent crimes, wars and other nasty things that go on in this world a likely assumption is that these criminal groups or individuals only gain more power because of the absence of a central authority or power. Thus a tyran could rise with absolute power in the midst of chaos promising justice and what not to its fearfull people. I think that the present state of the world has little to do with whether Plato is right or not, it is simply a deduction of how a state of government passes from one phase to the other and the psychological effect of its citizens with each phase.
Same as why he's right on democracy that it is a degenerative form of previous governmental systems. People are more individually focussed on their own desires and pleasures, profit means everything today to the point that we ignore ecological consequences of short sighted gains and interests.
AI is great I agree but we are far from replacing jobs with AI on a mass scale. Plus the transitioning will require a lot of adapting from societies around the world, even if AI would go really fast, humans are likely incapable of switching just as fast.