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.
Well, that depends on whether or not you care about "store now, decrypt later". Will the info you're sending now be totally uninteresting in 5 years? Great, you're probably good. Do you still want it to be secret in 20 years? Implementing post-quantum cryptography might be urgent.
given how sticky crypto algorithms are, transitioning early is a really good idea. git is still stuck with SHA1, and there's plenty of triple DES hiding in the boring types of critical infrastructure that no one can update.
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.