However, I think there's more than a fair argument that fate plays a role in City. The notion of time having a shape, as the Guardian put it, suggests it. The currents in time that drew the two traveling groups together suggests it. Edith being ahead of her time, and having the right idea at the wrong time, suggests it. The word fate not being mentioned does not mean that it's unreasonable to interpret City as being about fate.
Well it might yet be necessary to define what is meant by fate here. But since this thread includes in the title 'the universe will unfold as it should', it seems likely we mean a supernatural force preordaining events. But that is not what is happening in City (not the examples you give anyway). The notion of time having a shape or currents seems to be an ad hoc "scientific" explanation for otherwise unlikely events. I.e. the opposite of fate. Nor is Edith being ahead of her time an example of fate. It is only from the time travelling perspective that it looks like her ideas are destined to come about. Indeed the story makes it clear that they are not inevitable if the wrong decisions are made "now".
If the posts you referred to have examples of fate in City perhaps you could post links to them as you suggested? I would be interested, Though we may need to get on the same page definition wise, as I am not clear where you are coming from.