Your steps/mm shouldn’t be that far off. So something else is wrong. The components are all very precise and they shouldn’t be off by 3%.
The stepper has exactly 200 steps / rev. There’s no way for it to be 199, 201, or 200.5.
The driver has exactly 16 microsteps/step. The chips are very good at counting.
The pulley has exactly 16 teeth (you can count them).
The belt has 2mm/tooth. This can be 2.01mm or 1.99mm, but it’s not a rubber band, it is reinforced with fiberglass and is very resistant to tension. You’re moving less than the desired, so stretch is not the issue.
So you should have exactly 100 steps/mm, except for belt stretch. I haven’t ever seen a belt have a pitch of 1.94mm/tooth, but you can count out 20 teeth and measure them yourself if you think that is the issue.
So changing the steps/mm is a bit like “teaching to the test”. You have made it harder to see the problem, but you haven’t fixed it.
Post some pics and pay close attention to how it moves.