How many backup devices is recommended to improve backup performance?
In order to improve performance of our SQL Server backups we backup to multiple backup files


Not generally, no. That is a special purpose technique that can help.


  big amount of threads waiting


Why would that cause a loss of throughput? Threads are normally an ample resource. Problems arise in certain configurations where you burn through hundreds and into the thousands of threads.


  based on [the] number of cores in the server


That would make sense if the backup operation was CPU bound. That could be the case. As long as it is IO bound it cannot help to target the number of cores with any setting.


  one of our server shows BACKUPIO and BACKUPBUFFER as top 2 offenders wait stats


That points to an IO bound backup process. According to my experience that is far more common than CPU boundedness.


  a big DB (several TBs)


The size of the backup does not play a role in throughput considerations. Throughput is performance per unit of time.

There mere presence of waiting threads does not normally affect other threads and operations on the server. Waiting threads do nothing.


  so I have changed the number of backup files to use 4 backup files instead


That was unfounded because the backup is IO bound. Targeting the number of cores is not a good target.

If you added 128 CPU cores, your backup would not become one second faster.

You might have increased performance but only accidentally.

How many backup files to use is influenced by many things. An easy way to find a good number is to simply test different values, including 1 (the most likely value for common systems).