On SQL Server 2016+, you can load-balance read-only connections. (Note: this does not work on SQL 2012 or 2014 AGs.)
The full documentation is available here.
Essentially, when configuring your read-only routing list, you would use syntax like this:
ALTER AVAILABILITY GROUP ag MODIFY REPLICA ON N'SQL16A'
WITH (PRIMARY_ROLE (READ_ONLY_ROUTING_LIST=(('SQL16B', 'SQL16C'), 'SQL16A')));
This will make your first routing option SQL to load-balance between SQL16B & SQL16C. The second routing option is to send read-only connections to SQL16A. If server B is offline, then just that one server is taken out of the rotation--so all read-only connections would continue to go to Server C.
Load balancing is done in a round-robin fashion, so connections will be routed, A,B,A,B,A,B, etc. Load balancing does not consider existing number of connections, existing server load, or anything fancy.
Best Answer
If you have added the cluster, as in the WSFC computer name, to DPM then this may not be correct according to the MS documentation and may explain why you have nothing to backup - https://docs.microsoft.com/en-us/system-center/dpm/back-up-sql-server?view=sc-dpm-1807
Try adding the Availability Group Replicas individually. DPM should detect the AG configuration automatically and, provided all replicas are readable, it should backup up according to the AG backup preferences.