From my understanding, you would not be allowed to sell an "S3 compatible storage" as a service based off of Minio or another AGPL licensed S3-compatible storage solution, especially if you modify the source code of minio in any way and then serve that to your customers.
If you use Minio or another AGPL licensed service internally to support your own product without a customer ever touching it's API, it should be fine.
What in AGPL prevents this? AGPL only forces you to open source your modified version of MinIO/whatever. GPL forces you to open source only if you actually distribute the modified version, which gets muddy in the context of network services, therefore AGPL was created. If you want to build a commercial service based on AGPL software, there is nothing stopping you doing that.
If you use Minio or another AGPL licensed service internally to support your own product without a customer ever touching it's API, it should be fine.