How to find the last data backup on secondary replica?
The differential_base_time and lsn columns in sys.database_files indicate the point in time and in the log stream when the last non-copyonly backup was taken.  So:

select min(differential_base_time) last_full_backup_utc, 
       datediff(second,min(differential_base_time),SYSUTCDATETIME())/( 24*60*60.) days_since_last_full_backup
from sys.database_files
where type_desc = 'ROWS'
and is_read_only = 0


If you have read-only filegroups a backup will not update the differential_base_time, so ignore those.