I bought ETH on PancakeSwap using Smart Chain, and the transaction was confirmed and
received a notification on the app, but the funds are not in my Ethereum wallet.
PancakeSwap connects to your wallet via BSC network, that means the assets you buy/sell are on the Binance Smart Chain network.
The token you have received is a Binance Pegged BEP20 token.
You can manually add the supported coin/token to your wallet.
Search for ETH and look for the one that has Binance Pegged or BEP20 on it.
Every time you see a coin on PancakeSwap, or tokens that are well known to be in other blockchains, remember those are Binance-Peg tokens and in case you buy them they will show up in their respective BEP20 wallet.