I am a longtime Synology user (like you, I don’t enjoy having to run my main computer to listen to music). I’m not (yet) a Roon user but I did investigate what it would take to get it on a NAS a few months ago.
The first thing you need to do is create shared folders on your Synology to store your music. You can use whatever organization makes sense to you. For instance, I am mostly a classical music listener so I have four folders for classical music (classical_A-F, classical_G-M, etc.) and other folders for rock and folk. The main thing is that these must be shared folders; creating a shared folder in Synology is different than creating a normal folder.
Log into your Synology, open File Station, and choose Create/Create New Shared folder and follow the prompts.
I assume that you have your music files on a computer, probably stored by artist and album. Once you’ve created all the shared folders you want, you can copy these music files onto the NAS. You probably can drag and drop them, or you can go into File Station and use the Upload function. You certainly can do bunches of them at once, not one at a time. The individual folders don’t have to be shared (i.e., if ‘rock’ is a shared folder, you can create folders within it using Create/Create Folder); dragging/dropping or uploading folders from a computer into ‘rock’ will be fine too, since folders created that way are normal (not shared).
If you cannot drop and drag from Windows Explorer or the Mac Finder, the issue is almost certainly one of permissions. Windows or Mac OS may want you establish some login credentials the first time you access the Synology this way. It’s been a long time since I went through this so details are hazy.
Getting Roon on a NAS is not simple. I suggest getting your music in place and making sure that you can play it to the Bridge using a normal UPnP control point before tackling Roon. To do so, you need a server installed on your NAS. Synology makes one called Audio Station that you can install through the Package Center. Audio Station is not, IMO, the best server for Synology (that honor goes to MinimServer), but since you are new to this let’s keep it simple. Install Audio Station and then get a control point app on your iPad. Mcontrol is a good one (or is it mconnect?? I can never remember the difference between those two, which are made by the same company! Somebody remind me.). Audio Station should be visible as a server in the control point; choose it and also tell mcontrol to play to the Bridge, not to the iPad. At this point you should have music.
To meet your goal of not running your computer while playing music using Roon, you must install the Linux version of Roon onto the Synology. If you have Roon on your Mac, dragging it onto the Synology does not accomplish this. Roon suggested (last time I checked, 2-3 months ago) a SSD in the NAS in order to get acceptable performance from the Roon database; storing music files on spinning discs is good enough. You need to go to the Roon site for the download you need and specific instructions. Unless you have a specific reason for using Roon, you may find that using a server on the NAS plus a control point is all you need.
Let’s get you going with Audio Station and then tackle Roon. Come back with more questions.