### Tasks
- [x] `toggleBroadcastInput` isn't in the default settings
- [x] The cursors forget to keep blinking if you focus each pane and then unfocus them
- [x] They don't stop blinking when you unbroadcast
- [x] Broadcast border doesn't appear when you make new panes, but they ARE broadcasted-to!
- [ ] Broadcast doesn't work if you use context menu paste
- [ ] https://github.com/microsoft/terminal/issues/16287