From our perspective, it is not even an option to NOT consider Ethereum PoS as canonical Ethereum, so we suggest not executing any on-chain action concerning any type of PoW fork.
Regarding the liquidity protocol, as we explained in our analysis BGD. Technical analysis Aave <> Ethereum's PoS Merge, there is no infrastructure assurance on any potential fork, so current users of Aave Ethereum should not transact in a non-PoS Ethereum.
In what affects the Aave governance, everything around it (AAVE token, all the different UIs accessing it) will be working on Ethereum PoS, so in practice, there should be no activity on any fork. E.g. the AAVE token will live on Ethereum PoS.
It is important to highlight that the Community Guardian of the Aave Governance on Ethereum only has to cancel permissions, so there is no mechanism to do what is described, only with important technical overhead/development, which in our opinion is definitely not worth it.
In summary, from a technical/practical perspective, there is no substance on any potential non-PoS fork of Ethereum post-merge, so it should be implicit that Aave “accepts” PoS Ethereum, because it is the only Ethereum.