You’d do this the same way you process any task in SQL Server that requires massive scalability— with scripting. You can use either T-SQL or PowerShell. You don’t describe whether these databases are all on one instance or spread across many. So, let's assume the worst and that these are databases spread across multiple servers. In this situation, my approach would be to create a table with source_server and source_database as well as target_server and target_database. Then, I would write a script to iterate through the list of databases, running each backup from the source to each target, measuring their time and data volume, letting me know whether they succeeded or failed.
I believe that dbatools.io already has a script to do the backup and recovery test. So, all that you’d need to do is build the table to hold the source and target info, and the script to pipe those values into the DBAtool.io POSH script.