Sends this node's broadcasts to the workers on other nodes, one producer per pool group.

Every broadcast is written to a ring buffer of the last buffer_size messages. For each remote node the producer keeps a read cursor: the position up to which that node has acknowledged. A flush sends each node the messages from its cursor to the write cursor, and the cursor moves only when the node's worker replies :ok, so a failed batch is sent again on the next flush.

Remote calls run in tasks, so a slow or hung node never blocks broadcasts. A node is registered before its first batch:

• {:register, node, missed_writes?} when the producer has no cursor for it (new node, forgotten node, or this producer restarted), so a worker that knew this producer reports {:cursor_expired, node}
• {:resume, node} when the cursor survived and only the worker restarted

After a failed registration or delivery the node is probed with :ping and is retried only once it answers, so a hung worker does not pile up one copy of the call per retry.

A node more than buffer_size messages behind gets {:expired, node} instead of messages it can no longer be sent. Local subscribers never go through the producer: Phoenix delivers local broadcasts directly.