The public key is only written to the blockchain when you spend coin from that address, so at that point a QC can attack the key. Thus it's important to never re-use an address once you've spent from it and always spend the entire amount by using a newly generated change address.
As Canada points out[1], there is a window when it's revealed to the mempool but not yet committed to the blockchain. During that time, even a single-use address is not QC safe.
It would be an expensive endeavor since it involves throwing away solved blocks, but could of course package many QC safe(r) transactions so probably a profitable service in a QC compromised era.
How does that work? Anytime you spend coins from an address you hope you spend the exact correct amount that was already there? You pay 2x transaction fees to have to transfers - payment as one and remainder as the other and hope they both pop in the same block?
You can also send the change to a new address instead, which is how single use wallets work. You generate a new wallet, send the change to the new wallet and replace usage of the old wallet with the new one.
Another possible way would be to use a rotatable key derivation algorithm, where you can provide the 12 word phrase plus a number n, and it will provide you a different wallet for each value of n. Of course the key derivation algorithm must be quantam secure for the security benefit to apply in this context.