The essential idea is that rather than attempt to choose any one post-quantum-secure algorithm as a replacement, instead, bitcoin ought to support a set of various algorithms, and let end-users decide which one algorithm or combination of algorithms, best fits with their use-case, security requirements, and trust for different algorithms. In short:

A wallet chooses one or more public keys from one or more approved signature algorithms.
This ordered public-key bundle is serialized canonically and hashed to form the address.
Senders do not need to know which algorithm or algorithms are behind the address.
At spend time, the spender reveals the public-key bundle and provides one valid signature for each key in the bundle.
Users who want higher assurance can use heterogeneous algorithm families, while users with lower-value or high-frequency wallets can choose cheaper single-algorithm profiles.

This agile approach, inspired by TLS, SSH, and IPSec (all of which support multiple suites of different algorithms) has many advantages:

It defers the decision of which algorithm to use and trust to the future, when there will be more information available. Bitcoin developers can't predict what future algorithm breaks might happen, and enabling users to decide absolves Bitcoin developers of having to try to predict the future.
It enables rapid migration to other algorithms, should any future cryptographic break or even suspicious of possible future breaks, occur in the future, without having to wait for a new consensus for a change to the Bitcoin software and protocol.
End users can choose security levels that correspond to their security needs and spending habits. Have a cold-wallet securing millions of bitcoin which you spend from once per decade? Use several PSQ algorithm families with large key sizes, and pay higher transaction fees for those rare occasions you move funds. Have a small spending wallet you use to make online purchases? Use the smallest key size possible to save on transaction fees.