Spiking neural networks (SNNs) are promising for neuromorphic computing, but high-performing models still rely on dense multilayer architectures with substantial communication and state-storage costs. Inspired by autapses, we propose time-delayed autapse SNN (TDA-SNN), a framework that reconstructs SNNs with a single leaky integrate-and-fire neuron and a prototype-learning-based training strategy. By reorganizing internal temporal states, TDA-SNN can realize reservoir, multilayer perceptron, and convolution-like spiking architectures within a unified framework. Experiments on sequential, event-based, and image benchmarks show competitive performance in reservoir and MLP settings, while convolutional results reveal a clear space--time trade-off. Compared with standard SNNs, TDA-SNN greatly reduces neuron count and state memory while increasing per-neuron information capacity, at the cost of additional temporal latency in extreme single-neuron settings. These findings highlight the potential of temporally multiplexed single-neuron models as compact computational units for brain-inspired computing.