Good question! I did a small experiment: trained a small logistics regression from embedding vectors into 1st/2nd/3rd character in token: https://chatgpt.com/share/6871061a-7948-8007-ab53-5b0b697e90...

I got 0.863 (for 1st)/0.559 (for 2nd)/0.447 (for 3rd) accuracy for Qwen 3 8B model embeddings. Note the code is hacky and might be wrong in ways + in reality transformers do know more because here I utilize only embedding layer. However it does show there are very clear signals on characters in tokens in embedding vectors.