We are performing backup recovery on the primary. Does this mean our standby must be rebuilt?
It depends what happened.
Generally you don't need to rebuild the standby if you can restore any missing archivelogs to the standby and continue applying from the primary.
As the primary DB has been opened with resetlogs after restore and recovery ,you need to flashback the standby database.
If the flashback feature is not enabled at the Standby, it needs to be recreated by taking the fresh backup of the Primary . ( Ref: Doc ID 824213.1)
For creating the Standby DB , you can refer the below Article :
Doc ID 789370.1 -- Creating Physical Standby using RMAN Duplicate Without Shutting down The Primary
You can skip the configuration steps like creating password files, setting up SRL etc.
You seem has mastery on the subject
How do I know if flashback is enabled? Does flashback put more stress on the standby db, like storing more achivelogs history, and need more diskspace, and perform more background processes? Can I enable and disable flashback anytime to suit my needs depending on the situation?