I would say neither - it’s a constant d.c. with a constant, probably quite high frequency, alternating noise component superimposed on top of it. That noise is finding its way into the ADC, probably via the ADC reference voltage which is the 3.3 V supply rail, and the reference isn’t steady. In effect, it’s the ADC that’s adding the noise to the signal it’s trying to measure. If you want a mechanical analogy, think in terms of measuring the length of something with an elastic tape measure - while the tape measure is stretching, you’re not reading the true length.
If the new supply doesn’t help, I’d go for (2) first, then (1) as well if (2) wasn’t good enough. If you’ve only got less than 3A, you can have a lot more than 3 turns for your primary winding of the c.t.