The DS4xx is 4-bay one...
However, completely silent is still on the table. But not with a synology, since the price would be outrageous.
The Samsung 860 QVO 1TB is, right now, the cheapest disk with
€0,105/GB for the 1 TB.
€0,114/GB for the 2 TB one.
€0,157/GB for the 4 TB one.
That means you can DIY a system with a cheap motherboard, large heatsink. Almost passive system. Some open source firmware. (€200~ I guess)
6x1TB (€660~) for 5 TB storage RAID5.
4x2TB (€940~) for 6 TB.
3x4TB (€1500~)for 8 TB.
Compared to a similar load with WD RED 4x2TB (€320) or 4x4TB (€480) for 6 and 12 TB of storage, you're a whole lot cheaper.
Note the 4TB WD RED are noisier than the 2 TB. You could also spend some money at the hardware store and build a decent cabinet to sound isolate the box, and place it on turntable damper feet to prevent conducted rattle on the shelf it's on.
Don't try hardware raid with ssd's, check the support list before purchase