While using wagmi, I won’t recommend using any external wallet with web3auth interface. I would recommend using their direct connectors for the specific wallet. This is because the web3auth wagmi connector basically extends the web3auth provider connection with the wagmi interface. It works well with social logins since they exactly follow the web3auth provider connections, however, external wallets basically extend their provider into web3auth, which in turn is extended to wagmi. There are chances that some features might be affected in that case.
Ideally while using wagmi, I’d recommend just using web3auth social logins. Rest all wallet interfaces can be used using their own connectors that are readily available.