Can you please confirm you’re running you Aux Copy with “Scalable Resource Enabled”?
If not, you can kill the running Aux and run it ensuring Scalable is enabled
https://documentation.commvault.com/2022e/expert/11492_performing_auxiliary_copy_operation.html
By default the AuxCopy with scalable will process 1000 jobs at a time, this can be modified by increasing the batch size in the Scalable Resource Tab
https://documentation.commvault.com/2022e/expert/93901_online_help.html#b93902_auxiliary_copy_advanced_scalable_resource_allocation_online_help
In addition when Scalable is enabled, you can control how often new data is picked to be copied while the job is running, by default this is 45 minutes and can be reduced down to 15.
This will ensure that any idle streams will be re-populated if new data is available.
https://documentation.commvault.com/2022e/expert/11015_media_management_configuration_auxiliary_copy.html
Minimum interval in minutes for picking new data for Scalable Resource Auxiliary Copy job
Default Value: 45
Range: 15 to 360