There are many speculations that ETH will directly give its PoW strength to ETC after a successful merge. However, there are other many mineable cryptos that are easier and cheaper in the proof of work process. Since Ethereum is the leader in Web3, NFT, GameFi, and Defi its classic version could still handle its old PoW feature.
Miners have two plans for ETC price change. If ETH2 pushes ETC they will start mining Ethereum Classic. In another case, they will just stick to ETH1 by ignoring both ETH2 and ETC. Currently, ETC is not growing as high as ETH because of insufficient recognition.