what is best practice to migrate the backup data from old library to new library

hello ​@Ajal 

I don't have all the details, but I believe the exagrid team makes a valid point.

Commvault generally does not recommend using other hardware or software deduplication solutions in conjunction with Commvault deduplication.

The reason is that using a secondary deduplication application (either hardware or software) on top of Commvault deduplication can lead to unnecessary performance overhead and resource consumption, with no additional benefit. This means it’s important to choose either hardware or software deduplication before migrating to avoid complications. I would recommend evaluating and comparing the deduplication and compression efficiency of each option to ensure the best results.
 

Additionally, I would not recommend taking a fresh backup from the client side, as this would place unnecessary load on your resources. Auxiliary Copy operations are generally a better choice, as they don’t require a new backup to be taken from the client, but instead, they move data efficiently using the existing backup storage and media agent resources.
 

Regarding the Auxiliary Copy: If deduplication is not enabled for the secondary copy, the deduplicated data will be "unraveled" or "exploded" during the copy process. If deduplication is enabled for the secondary copy, a separate deduplication database is created for it, and the data will be deduplicated for the secondary copy.

If deduplication is enabled but the DASH Copy option is disabled, the data will be unraveled on the source side before being deduplicated on the destination side.

I hope this suits your needs! 
Best Regards,
Mohamed Ramadan
Data Protection Specialist

Think of deduplication as of archiving and compressing a file via Zip, Rar. 7Zip, you name it.

What are the benefits of double zipping any file? None, the second operation will not add any size reductions and only add complexity to the operation.

The same happens with deduplication, as ​@Mohamed Ramadan as advised, you normally choose a deduplication technology and stick to it, letting the appliance do its thing with the “raw” data.

In terms of moving data to another library, I once more agree with ​@Mohamed Ramadan , the best approach will be to configure a new library on the new Storage, and set this as an Aux Copy, if you want the appliance to deal with deduplication, make it a non-dedup Aux Copy.

Once all data is copies over, you can promote it to Primary if needed.

Deduplication on a Copy should not have any effect on any other Copies, since each Copy will have its own DDB taking care of how deduplication is done.