ETH is not afraid of doing hard forks, so I'm expecting that they will lead in adopting post quantum cryptography. And then BTC ecosystem participants can learn from ETH.
even if btc does a hard fork, you'll need to "reshim" the encryption on each wallet. and you can only do (n) tx per block. and only 1 blocks per unit time. this limits the speed of bitcoin moving to PQC, it must take at leaat ~3 years iirc