I’d DIY it (maybe with FreeNAS, about which I know nothing) instead of buying a proprietary NAS in a box. What’s the point of self-hosting if you’re going to be at the mercy of someone else’s software anyway? If you’re DIY’ing, there are 3.5" drive enclosures with soundproofing stuff in them that should keep the drive pretty quiet. Or if you can afford enough SSD’s for your storage requirements, then use those.

In the backup world, 50TB isn’t really a lot, and you’re not really ready to talk about tape systems or maintaining an always-on disk system. Also, HDD’s have been getting more expensive due to AI idiocy. But, cheapest is probably a second raid system, like 4x 20tb drives. Do the backup at home and then move the backup system off site and either keep it spinning, or make sure to spin up and test the individual drives every so often.