Remove entirely-redundant synchronization inside of Broadcaster.

Per <https://docs.rs/tokio/latest/tokio/sync/broadcast/struct.Sender.html>, a `Sender` is safe to share between threads. The clone behaviour we want is also provided by its `Clone` impl directly, and we don't need to wrap the sender in an `Arc` to share it.

It's amazing what you can find in the docs.

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