For the network part, a daemon outside the sandbox serves a filtering HTTP proxy on a Unix socket. I mount the Unix socket into the sandbox and bridge it to localhost with socat. With the net namespace unshared, the app can't reach the network at all except through this proxy, which only allows LLM providers.
By separating the coding tool from the LLM provider, I feel safer: the coding tool cannot leak anything on its own. It can only talk to the LLM provider, so a real leak would require the provider to be complicit too. And any sensitive files, inside or outside the project, are hidden by the mount namespace, which I suppose is hard to escape.