This looks wonderful, I've dreamt of something like this back when I was in academia! You mention some advanced stuff like abstract index notation which is usually the hardest part to get right with things like simpy and even mathematica, how does your package handle simplifications of complex tensor expressions (GR, hydrodynamics, etc.)?
You can specify symmetry/antisymmetry patterns for tensor index slots and it takes advantage of that to speed up the calculations. This part was pretty important for me so i spent some time thinking about it. I wanted to try to put xACT’s patterns in but it would have been quite the undertaking.