repmgr 4.x provides support for monitoring BDR nodes and taking action in case one of the nodes fails.
Note: Due to the nature of BDR, it's only safe to use this solution for a two-node scenario. Introducing additional nodes will create an inherent risk of node desynchronisation if a node goes down without being cleanly removed from the cluster.
In contrast to streaming replication, there's no concept of "promoting" a new primary node with BDR. Instead, "failover" involves monitoring both nodes with `repmgrd` and redirecting queries from the failed node to the remaining active node. This can be done by using an event notification script which is called by repmgrd to dynamically reconfigure a proxy server/connection pooler such as PgBouncer.