Remove usage of `jsonrpsee::RawClient`

By using a `jsonrpsee::Client` we are able to remove all the shared
mutable references required when interacting with the RPC server. This
is convenient as trying to sharing mutable references in code that uses
async/await is a bit of a pain.

However, using a `Client` instead of a `RawClient` is not yet supported
by the `jsonrpsee::rpc_api` macro, so a fork must be used for the moment.