What obstacles do you tend to run into? I'd be inclined to use a Chinese model for that, since Claude was presumably RLHF'ed primarily by native Anglophones.
Have you tried a Chinese-trained LLM for learning Mandarin, and if so, did it help?
I think to learn a language you need to do as many modalities as you can: Speaking, listening, reading, singing, asking questions to native speakers, asking questions to LLMs, writing, flash cards, etc.
The obstacle with LLMs is that they are specifically going at their own uncanny valley pace. I do see how that might be not a problem for some prompts.
I haven't tried a Chinese-trained LLM for learning Mandarin, so I'm not sure which LLM is best..