I suspect you are using Taquito's Contract API, but the Wallet API should be used to interact with a wallet.
const contract = await tezos.wallet.at(contractAddress);
Instead of :
const contract = await tezos.contract.at(contractAddress);
More details on the wallet API here: https://tezostaquito.io/docs/wallet_API#calling-a-smart-contract
wallet.connect seems to indicate you are using the @temple-wallet/dapp package. If you are using TypeScript, there is the TempleDAppNetwork enum that you can import from the package with all the different network names. With the right settings on your editor, you should get a list of the network names when you type the parameter of wallet.connect :)