1. What version of vSphere are you using? If it's a paid version there will be different APIs available than if you're using the free version.
7.0 U2 Enterprise Plus, courtesy of my generous employer. (Although I suppose it's not entirely altruistic, since the assumption is that I will tinker about on my own time, learn new things and then use them in my work...which is of course exactly what tends to happen!)
2. Can the Synology take snapshots of the iSCSI share and put them somewhere?
Yes to the first; I don't think so to the second. I spent a ton of time going down that rabbit hole and could never find a viable solution. You can save snapshots to a locally attached drive, but that's no good to me. Or you save snapshots to a second NAS, but that's no good either. For whatever reason, it doesn't seem to be possible to export (or import) snapshots via SMB, FTP or anything else to/from just a regular, network-accessible location.
3. Is the Mac Mini running Server OSX or something else? It'll determine what options are available.
Just regular macos Mojave.
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You can separate the storage repositories from the management server and from the backup processing hosts or keep them all together. It scales well, but a "mac mini" as a backup server is likely way too underpowered to do anything useful. You need decent memory and good random IO SSDs to handle the backup processing well.
The mini has 16 GB of RAM and an SSD, is recognized by Veeam as a remote SMB backup repository, and Veeam says that the primary bottleneck is the source. I infer from this that the mini is an adequate backup target.
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What about it doesn't work? Costs? Licensing issues? Backups fail to run?
Costs/licensing is a non-issue: I'm using the free version limited to 10 VMs because that's really all I need right now. The problem is that backups were either failing to complete about 70% of the time (from when I first started using it up until about a month ago), or failing to complete 100% of the time (the last month). I don't care to go into any more detail - I've spent too many frustrating hours trying to figure out why at this point - I just want to back this up some other way.