This is really difficult to explain. The tone of voice, inflection, cadence, emphasis, pitch and even the comma (pause) all make a difference.
Both of those sentences can have the same meaning you described, or they can have the opposite meaning. They can also just be asking a question, or be judgmental and condescending.
You really need to hear it said in different ways, but I’ll make an attempt to describe it. I’ll do the second one first.
You don’t still believe that, do you?
You still don’t believe that, right?
When delivered in a flat voice with a pause, this is a verification and nothing else. The speaker thinks they know that the other person no longer believes it, but asks for verification, maybe just out of curiosity. There is no judgement, no surprise.
You don’t still BELIEVE that do you?
(slight raise in pitch on “do you”)
This is more judgemental. This almost has the feel that the person should never have believed it in the first place. It shows some surprise and judgment, like the person must be really dense to believe it all this time. It’s more of a statement than an actual question.
You don’t STILL believe that do you?
This is only somewhat less judgemental than the previous one. The previous one was highly judgemental that the person ever believed it in the first place. This version is less judgemental that they believed it in the past, but is somewhat surprised and slightly judgemental that the person still does.
In the above three example, the first one takes on the meaning that the person no longer believes it. The second two examples have the opposite meaning, that the person does still believe it.
You still don’t believe that, do you?
You still don’t believe that, right?
Like before, when it’s delivered flat, with a pause, it’s merely verification, with no judgement. The speaker thinks the other person no longer believes it, and is asking for verification.
You STILL don’t believe that, do you?
This one also means the speaker thinks the other person no longer believes it, but is more judgemental. It leans toward a statement, instead of strictly a question.
You still don’t believe that?!!! (higher pitch with exclamation)
This is strong surprise, and may or may not be judgemental.
OK, so that’s pretty complicated to describe in text. This is the reason why people started using emotes online. It’s so easy to misunderstand the meaning online. It’s not only text, but you may not know the person well either. Those emotes got so over used for a while that people quit using them because it just wasn’t cool any more.