To the last two people that replied: I don't know how this works on Mac, but on Windows when you install an audio interface out-of-the-box, you only hear audio from ASIO-based applications that have explicitly selected that interface as the audio device. If you use an audio application without ASIO support (like a web browser), you hear that audio through your computer's built-in audio hardware/headphone jack. So unless you use special hardware or make some settings changes, computer audio is going to come out one set of speakers/headphones and DAW audio is going to come out another. (In my setups I sometimes use a USB headset for computer audio and my studio monitors/headphones for DAW work.)
One way to address this is to change the Windows settings to use your audio interface as the default audio device, which merges computer audio plus DAW audio into the same output. But this isn't great to do, since it can take resources from the interface and/or introduce some audio instability. And also, who wants to hear mail notifications while they're tracking?
As mentioned in my post, I use a monitor controller which lets me merge the signals outside of my PC, so my audio interface is still fully dedicated to Cubase but I also don't have to change anything in order to hear both Cubase and other computer sounds over my studio monitors; don't have to switch outputs/speakers/headphones, etc.
Oh okay, yeah, I'm on a Mac so things don't tend to require drivers, everything just works straight out of the box and universally: global audio output setting sits in the menu bar at all times, and it's each software's
own settings where you'd
separately make an exception to that rule. But for example, since I don't want that, my DAW outputs are simply set to "System setting", i.e to follow whatever that is at that moment. Some DAWs ask if you want to use the device as an output if you switch them on when the DAW is running.
There's software that allows managing audio routings if you want to specify which software sends to which output, but I'm afraid I have nothing to suggest for Windows.
But by the way it sounds, I would select the interface as a universal output, unless that somehow isn't possible and the second option would therefore be to have separate speakers for audio work vs. other stuff. Especially if you need to reference other audio content, go online for tutorials or inspiration quite frequently, it just doesn't seem very practical to
not use the audio interface as the global output.
I haven't heard of using the interface as global output leading to meaningful lag or audio instability; is it a common thing in general or just on Windows? Also, it also must depend on how the interface is being used, i.e is it just an output device or is there also input and monitoring going on. There's also quite a bit that you can do for memory management on a computer, and the real hog should be the actual DAW; and how heavy projects people make varies dramatically.
And also, who wants to hear mail notifications while they're tracking?
Or, who wants to hear any notifications, especially on a computer where you can probably see the notifications because you're already sitting there?

I don't know how Windows handles all that, but on modern Macs, in theory, there's now different focus modes that can be activated (much like on a phone) that silence notifications, or only deliver stuff in the background quietly in order to not disturb you during work, or only allow notifications from selected contacts. I've never kept any audio notification sounds on for my computer, except for some instant messenger, and that too only when the software is actually open. But recently in the world of distractions, I've had to go even further, and I occasionally find myself disconnecting the internet router in order to get work done; almost nothing is so urgent that I would require information on as-it-happens basis, rather than being able to check back in a few hours.