Yes. Pretraining and fine-tuning use standard Adam optimizers (usually with weight-decay). Reinforcement learning has been the odd-man out historically, but these days almost all RL algorithms also use backprop and gradient descent.

Are LLMs still trained by (variants of) stochastic GRADIENT descent? AFAIK what used to be called "backprop" is nowadays known as "automatic differentiation". It's widely used in PyTorch, JAX etc