I wonder if there's a bit of survivorship bias with this one. I've never been able to learn relative pitch after trying quite a lot of different methods, ear training app and playing a couple of musical instruments. If you're in a music school then perhaps your baseline musical ability is already relatively high?
I really doubt it, and I am not surprised that apps didn't work. I also don't think playing a musical instrument actually gives as much insight here as you want - it's a very indirect transfer if you're learning via classical methods or if you are learning purely by reading. Jazz and contemporary methods involve a lot more "listen, then play back" rather than reading. If you want to work on ear training and theory, cross-training with some jazz or contemporary helps a lot.
The way music schools teach this is relatively brutal and annoying, with a _lot_ of repetition and testing (eg "sing a major second above this note" and "identify the interval" questions), but I am not sure any other method works. At the same time, everyone going through an ear training curriculum does pick up decent relative pitch. This can take a year or two for college music majors, so it's not exactly a casual exercise. However, I assume the major barrier to entry is not musical aptitude but willingness to put up with bullshit, because it feels like bullshit when you are doing it.
That sounds like a the ear training I have done but even after a couple of decades I don't have any real ability to tell the difference between intervals. For example, I listen to a musical interval and try singing up the major scale to match it but everything matches a fifth (in my internal melody). More recently I found the Sonofield app an interesting idea for learning the intervals but wasn't able to gain any consistency.
I remember many years ago in my music lessons being shocked that some people can hear multiple notes played simultaneously. I've never found much material on learning this skill.
Learning intervals by quotation can work. "Comet, it makes your teeth turn green" starts with a descending third and is a very memorable song.