Refactor `MultichainRouter` to not use `withKeyring`

[GuillaumeRx]

withKeyring acquires a mutex lock when sending a request, that means that anything that requires the withKeyring in one of the Snap RPC calls (like snap_getBip32Entropy) will be hanging due to the deadlock that the router creates.

As of today, a temporary fix has been done on the extension side to avoid that issue: https://github.com/MetaMask/metamask-extension/pull/32120