To my knowledge none of the players is even profitable on inference, though Google probably is, considering the continuous release of papers around kv cache optimizations, mtp etc.

Your knowledge is off. Inference is highly profitable - at least for OpenAI and Anthropic.

I'd be delighted if you can link to actual numbers supporting this assumption, as all reputable reporting says OpenAI's revenue is smaller than their inference cost, e.g. https://www.ft.com/content/fce77ba4-6231-4920-9e99-693a6c38e...