wing Welcome to Piano Tell!!
I can really relate to your post. I used to do a fair amount of exercises as well, but now I almost never do. My practice is highly repertoire-centric, and at this stage, I don't think I suffer from it. So I think you can move forward with taking exercises off your practice menu without worrying about.
However, I will say that having a good teacher, someone who is a good fit, is essential. With a teacher, I've been able to learn and polish pieces that I either wouldn't be able to do at all on my own, or that I wouldn't be able to do as well on my own. None of my recent teachers have pushed me to do exercises either, and all have agreed with my repertoire-based approach. So I'm sure there's a teacher out there who will work for you. And in my opinion, the benefits of having a good teacher are well-worth the effort it takes to find. Especially if you want to work on Inventions.
Now, as to your main query, and at the risk of sounding contradictory, I probably would not get rid of many of those books. Maybe that's because I'm addicted to music books For one thing I like having lots of books. For another, I've found over the years that I sometimes am looking for something, and I have it in one of those books. So even if you're not working through the exercises regularly, it might be good to keep the books. One of the biggest uses I've found for books I bought years ago is that I later end up using them for sightreading practice, so that's something might consider.
So with that said, here are my thoughts:
ok, maybe get rid of this one.
Isidor Philipp (independence exercises)
Beringer's Daily Technical Studies
Keep these if they look like they could be future sightreading material (I'm not familiar with them), but otherwise they can go.
Dohnányi's Essential Finger Exercises
Maybe get rid of this (I would)
Berens Training of the Left Hand
Not familiar, but I wouldn't keep such a specific (and therefore limited) book, I think.
Czerny (I have several of his books and I find them dreadfully boring)
Brahms' 51 Exercises
Liszt Daily Exercises (intense!)
I think I would keep these, future sightreading and such well-regarded materials that you may want to refer to them in the future.
Not familiar
Burgmuller Etudes (op. 100 – I actually like these)
Definitely keep this (first, because you like it and second because it's definitely future sightreading material)
I also have various jazz exercise books too, for stride piano and ii-V-I patterns. Again, why not just play some tunes...
I would also keep these, they could be a helpful reference to you in the future.
Again, this is what I would do, but I love having tons of music books. If you feel like the space is really needed for something else just move them somewhere else in the house you might decide to get rid of a few.
P.S. good luck! Getting rid of books is awfully hard!