A terminal Ctrl+C is delivered to every process in the foreground process
group, so a server spawned in our group died on any Ctrl+C during a turn -
killing in-flight tool calls and leaving the connection dead until
/mcp reconnect. start_new_session (POSIX) / CREATE_NEW_PROCESS_GROUP
(Windows) puts each server in its own session/group instead.
Tests assert the spawned server's process group and session differ from the
CLI's (they used to be the same group).