I can't speak to what you're looking for specifically, however I can give you an idea of the level and type of noise you could expect.
With a local server I built with 3 standard 8TB HDDs, the "noisiest" part of the whole computer is the fans itself - it's very quiet compared to say, a fanned air purifier on full or maybe even half power. I've never actually heard my hard drives from any of the computers I've built in the last 6-8 years, and I'm usually right by them. If I listen very closely I may hear some ticking/spinning if they happen to be ramped up.
So under load, there may be a chance of hearing some of the spinning disks in a quiet room, however I haven't actively heard an HDD since 2012 - though the size you're going for could be different as you mentioned. I can't speak for the 18tb sizes. As for the smaller external HDD's, I have 3 6TB ones running in tandem and it's pretty much the same, I've heard them ramp up slightly but it's nearly silent even under load it's more of a gentle hum. If there were any noise sources like music it would be unnoticeable. But again, the size may play a factor.
You mentioned it's right by your bed but would your active hours align with the backups? I.e. if you run them overnight from 2a to 8a, you'd already be asleep for the backup. If it's noise that prevents you from sleeping that may help.