How to expose the connected wallet as an eip1193 provider to a different library?

[akshatmittal]

Basically title. There are many ways to connect a wallet to wagmi/viem, and I'd like to find a way to convert a client to an eip1193 provider, including the signing part managed by wagmi/viem.

At the moment I'm querying the connected connector and passing that as the eip1193 provider, but this isn't perfect and also doesn't expose a way to use private keys as signers via eip1193.

Ideal would be to do something like client.getEIP1193Provider() or something on those lines.