It's unlikely that any of the modern cryptographic primitives will break over night.
First, modern encryption isn't susceptible to "this one weird trick!" like the early days. ChaCha isn't even a cipher. It's a key stretcher. Which means, even if you broke the math behind ChaCha, its inherent complexity means its still widely dispersing the original key across the cipherstream. There just won't ever be enough key material recovered per cipherstream block to be a concern for anybody.
Take a strong password, encrypt all of your emails over your whole life with it, and I'll bet hard cash no break of ChaCha will ever recover that password.
I have zero concern for modern encryption being broken in any meaningful way.
Public key crypto on the other hand, that's _ripe_ for breaking. Most all of it is built on assumed "hard" math. AI could easily break that, and I expect it to. And public key crypto is all used in very transparent algorithms that, once the math breaks, fully expose themselves. So record HTTPS traffic today, crack the public key crypto later, and you can decrypt them easily.
That said, I would expect a break on public key math to occur _steadily_. i.e. an AI might find a solution to the hard math, but the solution itself will be intractable in practice. Then maybe next year's AI reduces the complexity of the solution, so maybe a supercomputer could factor ten keys a year. The year after that you get a million keys cracked per year. And so forth. Nothing close to overnight.
Meanwhile, if we have AI that is capable enough to crack that math, we also have AI capable enough to both invent better math and rapidly deploy that latest HTTPS and such globally.
If you look at elliptic curves I don't think there has been any big changes in attacks for 20 years but some attacks like MOV or SMART would have been fatal to EC if they had applied to more curves. So maybe there is some unknown attack that applies to all curves or applies to a small subset of curves that happens to overlap the curves we use. If you are super paranoid you should probably use curve25519 because then at least you can be confident it was not deliberately engineered to be weak. it could still be weak by chance but presumably the designers did not have enough flexibility to choose the parameters to make it weak. Some people are paranoid about the NIST curves because there is no verifiable explanation for where the seeds came from. But if the NIST curves were made weak then I think its a situation where theoretically anybody could find the weakness which is very dangerous. I don't think it was possible to create a no-body-but-us backdoor for the NIST curves.
Also, even if DLP is hard for the curves we use algorithms like ECDSA might be a bit fishy. Unlike schnorr signatures there is no proper security reduction for ECDSA.