It’s a Gm7 with an added sharp 5? I guess it’s not really an augmented chord, because the original 5 is still in there, it hasn’t been replaced by the sharp 5.
Would you call it a Gm7add#5? Gm7add b6?
It sounds … good to my ear, even though I would have thought having both the 5 and the #5 in at the same time would clash. There’s definitely some dissonance in it, but I don’t find it unpleasant. I actually think it has kind of a cool, mysterious quality.
It would simply be called a Gm7b13.
In essense, its a Gm13, but you’re just flattening the 6 (13)
The use of add#5 etc is not really appropriate here, as it denotes you are sharpening the existing 5th, which you are not. Much better viewed as a b13 (b6) in this instance.
A fairly common voicing in Jazz.