If you want minimum latency, you want the input side of an traditional vocoder, not an FFT. This is the part that splits the modulator signal into frequency bands and puts each one through an envelope follower. Instead of using the outputs of the envelope followers to modulate the equivalent frequency bands of a carrier signal, you can use them to drive the visualizer circuit.

That can be done with analog electronics, but even half an analog vocoder needs a lot of parts. It's going to be cheaper and more reliable to simulate it in software. This uses entirely IIR filters, which are computationally cheap and calculated one sample at a time, so they have the minimum possible latency. I'd be curious if any LLM actually recognizes that an audio visualizer is half a vocoder instead of jumping straight to the obvious (and higher latency) FFT approach.

For recorded music, you could always buffer however many milliseconds of audio to account for the processing.