OpenAI themselves must not have a "reasonable definition of L", then. Their own papers and press releases refer to GPT-2 (from 2019) as a "large language model".

https://openai.com/index/better-language-models/

Sure we do, since Fei-Fei Li and team created that annotated dataset, which allowed to train first LLMs. So LLMs are here for more than a decade already.