the problem is you're trying to solve three different things (outside noise, your girlfriend being around, notifications) with one generic solution. headphones aren't the answer, especially since you need to stay accessible for work.
start like this: have a clear conversation with your girlfriend about schedules. doesn't need to be rigid like "from 9 to 12 you can't make noise," but more of an understanding of when you're in meetings, when you're doing deep work. your apartment's small anyway, so if she understands that you need like 2 to 3 hours of focused time in the morning, for example, that makes a difference. it takes away the anxiety of her being there and you getting distracted worrying whether she'll interrupt you.
for headphones, use the strategy of pink noise or white noise at low volume - not music, that just distracts you more. spotify has playlists for that, or even a simple app like myNoise works. it masks neighbor noise without cutting you off from notifications. keep the volume really low, just enough. and about slack, set it to vibrate on your phone when something important comes in - most people don't know you can separate notifications by channel or person, so you only get alerts for stuff that actually matters.
last thing: move to a different spot in the apartment if you can. even if it's just a desk in another room, or near the window. your brain treats a new space as a different "work mode" from the couch where you watch series at night. and when things get too chaotic, do 50 minutes of focused work then 10 minute breaks - sounds basic but it breaks the frustration pattern of "ugh i wasted the whole day."