If you add H2O2 to your sulfuric acid, it will be contaminated with stabilizers such as sodium phosphate (perhaps Na3PO4), sodium stannate (not sure which one), phenol, organophosphonates, acetanilide, nitrate, benzoic acid, tetrapotassium diphosphate.
I’m not sure which one your brand of H2O2 contains.
If you need very pure H2SO4, distill it under a slight vacuum.
If purity doesn’t matter, add a little H2O2.
For making CuSO4 with the electrolysis method, there needs to be a decent amount of water in your sulfuric acid. I don’t think it works with 98% H2SO4.