(obviously it might take years for me to get good enough at something, or if you set the "arbitrary" task as something ridiculous, but lets work in good faith here and think of something the average human could do after learning about it)

If we progress to the point where an LLM instance can meaningfully learn to get better at something overtime without retraining, then I will accept that is basically AGI. Right now, they still seem to be pretty boxed into their training, even if you can prompt them to act differently.