DSM has three different fan methods that you can set (quiet, medium and "loud"). You can also install better fans, I think they cost around 40-50 CHF, which are then quieter. Generally, I'm currently using "quiet" and that's what the name says.

I currently use my ds918+ in the living room as a media server and data storage, and I have to say that I only hear it when I pay attention to it and it is otherwise rather quiet. Otherwise not.
So, I don't hear it during a conversation or a film, neither the fans nor the disks, at least I've never noticed it.

I also use Plex. Important to remember, generally media services (like Plex) prevent Hybernation mode, so you can't rely on not hearing it because it's in Hybernation mode.

I'll check again tonight, if it is audible I'll post an update. But it's a bit subjective anyway (at what level something is disturbing). If you want to be on the safe side, put it somewhere where it doesn't matter :))

The NAS (excluding the hard drives) is practically inaudible, but the volume of the hard drives is audible, but how much depends on how you use them. I used to have WD Red Pros and have now upgraded to IronWolf, both have 7200 RPM and are quite audible under load, which is why I moved the NAS from the living room to the office. But that shouldn't be a problem while watching films because the film is loud enough anyway, the volume is actually only audible when everything else is quiet and you want to take a nap on the couch, for example. In addition, the hard drives are of course only loud as long as something is accessing them, it also depends on what else is running on them apart from Plex and at what times the backup tasks etc. are running.
Otherwise, the data sheets of the hard drives also show the volume in decibels during idle and during a search. There you will see that a WD Red is about 20-29 dBA loud.

In the meantime, after two 4-bay NAS', I changed to a 5-bay and 8-bay NAS (also WD Red Pro), these are definitely (also) audible. It is questionable at what point someone finds the noise of the fans or the hard drive activities "disturbing".
It bothered me when, for example, a "quiet" film scene was playing and I then heard some kind of noise (fan/hard drive).

I have everything in a 19" rack in the basement, in a separate room where it doesn't bother anyone (noise / waste heat). Of course, you don't have this option everywhere. But I would definitely not place it in the same room where TV/movies are also watched - provided, of course, that another option is available.