Yes, although as far as COT goes there is no need to assume any similarity to human thinking. It's just about how many sequential steps - how long of a "chain of thought" - are needed to reason through and respond to any input.

Those steps could either be all internal (looped), therefore hidden, or with partial external visibility due to emitting a token every N steps. The complaint about Astra, and moving in the direction of hidden COT, is that it makes these models far harder to monitor and debug.

I agree that most of what these companies doing - synthetic data, etc - amounts to trying to squeeze all the juice out of the pre-training data, although the recent trend of RL post-training via agents running in custom task simulation environments does change that a bit - these environments, and the rewards they provide, are a new source of data.