Given how seriously the spookie parts of the US government are taking it, I would treat it with a similar level of urgency. While we obviously aren't privy to everything they know, their public actions indicate that they don't think it's a hypothetical risk, and is something that we will need to be ready for within the next decade or so, given technology refresh cycles: they need to get these crypto algorithms in place now, for devices that will still be in production use well in to the 2030s.

There's also a good chance that the initial compromises of the classical algorithms won't be made public, at least initially. There are multiple nation-state actors working on the problem in secret, in addition to the academic and commercial entities working on it more publicly.