LLMs are not inherently indeterministic. Batching, temperature, and other things make them appear so when run by big providers but a locally-run LLM model at zero temperature will always produce the same output given the same input.
That assumes they were implemented with deterministic operators, which isn't the default assumption when using neural network libs on GPUs. Imagine random seeds, cublas optimizations - like you can configure all these things, but I wouldn't assume it, esp in GPU-optimized OSS..