I haven't tested WD RED 6TB, i do own a 6TB Purple (similar but different firmware) and its not as quiet as 3tb RED, but its not super noisy either, i cant say for sure but there are time that it has a chirp but i also have a small 1.5 tb WD in there, never really bothered to see which of the two is creating that sound, that usually disappears if i reboot.
I would recommend to go the NAS Route, while today's disk are not super noisy as in the 80s / 90s,but not as quiet as WD Greens (single or dual platter) once were, and part of it is that they are cramping lots of platters on the disk, more than they usually did on air based, so its hard to expect quiet operation. With NAS like Synology that are compact, efficient and very good performing, i don't see a reason to maintain mechanical disk inside your desktop, but its up to you if you feel its worth it.
One practice that a lot are doing, including me, is we are buying WD EasyStore / MyBook / Elements USB hdds and shucking them to be used on our servers, this will bring considerable savings, if you catch a sale, its almost half the cost, and if done correctly you can still assemble back without issues in case you want to reclaim the warranty. In the past it had only WD Red 8tb (helium based), now a days, in all my purchases, i have gotten White Label drives, that according to storage forums, are the same as reds, weather the firmware is the same idk, but they are not 7200rpm drives. The issue for me, is that every day i need more space, so this is the only cost effective way i been able to sustain my servers.
The savings could easily be placed toward a nice synology =P, recommended intel based, the new low power celerons are very capable, check
DS218+ or
DS1019+.
WD has reacted introducing a 3.3v reset on this drives, that can be avoided doing either of two procedures, taping the 3.3v pin on the hdd, or using a molex power from your PSU and convert it with Molex to Sata, both of them work fine, and to my knowledge synology doesn't have a 3.3V power on their nas, so if this is correct, you dont need to do either of the procedures. I leave you a couple of videos in case you are interested,
How to Remove / Shuck the Hard Drive from Western Digital Easystore 8TB Drive
How to Fix the 3.3V Pin Issue in White Label Disks Shucked from Western Digital 8TB Easystore Drives