Sorry but that's false, you are confusing transformers as an architecture, and auto-regressive generation, and padding during training.
Standard transformers take in an arbitrary input size and run blocks (self and possibly cross attention, positional encoding, MLPs) that don't care about its length.
> They also have a fixed output of one probability distribution for the next one token.
No, in most implementations, they output a probability distribution for every token in the input. If you input 512 tokens, you get 512 probability distributions. You can input however many tokens you want - 1, 2048, one million, it's the same thing (although since standard self-attention scales quadratically you'll eventually run out of memory). Modern relative embeddings like RoPE can support infinite length although the quality will degrade if you extrapolate too far beyond what the model saw during training.
For typical auto-regressive generation, they are trained with causal masking/teacher forcing, which makes it calculate the probability for the next token. During inference, you throw away all but the last probability distribution and use that to sample the next token, and then repeat. You also do this with an RNN. An autoregressive CNN (e.g. WaveNet) would be closer to what you described in that it has a fixed window looking backwards.
But a transformer doesn't have to be used for auto-regressive generation, you can use it for diffusion, as a classifier model, for embedding text. It doesn't even see a sequence as spatially organised - unlike a CNN or an RNN it doesn't have architectural intrinsic biases about the position of elements, which is why it needs positional embeddings. This lets you have 2D, 3D, 4D, or disordered elements in a sequence. You can even have non-regularly sampled sequences. (Again this is for a classic transformer without sliding window attention or any other special modifications).
> (padding the unneeded context window with null tokens).
To have efficient training, you pad all samples in a batch to have the same length (and maybe make it a power of two). But you are working with a single sequence, the length is arbitrary up to hardware limitations, and no padding is needed.