I think what you mean is that in Buddhism there is no self beyond the self implied by your thinking mind. The nothingness you refer to is the eschewing of attachment to what isn’t and being simply what is. It doesn’t mean a void, it means that all existence is within the awareness, which isn’t directly observable and is constantly changing. As such, it’s effectively nothing - except it is literally all you are. Your past and memories are just crude encodings, the future is a delusion. Your self identity has almost nothing to do with who you actually are right now. Your dissatisfaction with your situation isn’t meaningfully different from your delight in some experience - they’re both transient, and are just experiences of the present. You can avoid unpleasantness, and enjoy pleasure, but holding onto and seeking or avoiding entangles your awareness in what isn’t to the determinant of what is. As you continue releasing the various attachments and let the awareness take hold, and actions come naturally without thought or attachment, you cease suffering and cease causing suffering.

But to my understanding the idea of nothingness being some objective in Buddhism isn’t the case - but it’s often described as such because that state of pure awareness without encumbering thought and attachment in many ways to an unpracticed person feels like nothingness. After all, the awareness is silent, even if it is where all thought and feeling spring from.

Finally, awareness isn’t that moment you snap back to thought. You’re always aware. We just tend to be primarily aware of our thoughts and emotions. We walk around in a haze of the past and future and fiction as the world ticks by around us, and we tend to live in what isn’t rather than what is. You don’t disappear in the sense that you cease to be as an individual mind, you are always yourself - that’s a tautology. What you lose is the sense of some identity that’s separate from what you ARE in this very moment. You aren’t a programmer, you aren’t a Democrat, you aren’t a XYZ. You are what you are, and what that is changes constantly, so can’t be singularly defined or held onto as some consistent thing over time with labels and structure. You just simply are.