I am using the following, this is only for a few servers but maybe you can adapt for your case :
1. Create an extra DB on your instance or use master to host your stores procedures, for since code to backup your DB (SP dbo.backup_db).
2. Create PowerShell script backup_db.ps1 with cmdlets "invoke-sqlcmd" to call your store procedure :
Invoke-Sqlcmd -Query $invoke -ServerInstance MACHINENAME\INSTANCE
Before this you will have to check your execution policy is "RemoteSigned" and import the sql module
3. Add, Program and Start your PowerShell script with the Windows tasks scheduler :
Action : Start a program. program/script: put the full powershell path :
Add arguments : put the script and his full path, do not use quotes.
Start in(optional) : directory where your script reside, without quotes
Works for me with success for months !