I am afraid there is no out-of-the-box option in azure devops to set the variable group on organization level, variable groups is in Team project level.
Until now, in our official feature suggestion for Azure Devops forum, there has been a such suggestion exist in it: Library of Variable and Task groups shared between all projects. You can comment and vote it there. Our PM and Product Group are reviewing these suggestion regularly and considering take it as plan.
As a workaround, you can use the Azure Key Vault task to pull data from Azure Key Vault. You can have as many Vaults as you like and use in one or all projects.
