Function run_agent_with_bin 

pub(crate) async fn run_agent_with_bin(
    bin: &str,
    agent_ref: AgentRef,
    task: AgentTask,
    tx: UnboundedSender<AgentEvent>,
) -> Result<AgentRunHandle, AgentError>

Internal entry point — same as run_agent but takes the claude binary path explicitly. Lets tests inject a known-nonexistent path to exercise the spawn-failure path without touching env vars (Rust 1.81+ flags std::env::set_var as unsound under concurrent test execution). The public run_agent is a thin shim that resolves the binary from $AGENTMUX_CLAUDE_BIN or the default.