Modern protocols loop back the reasoning tokens in raw textual form via an encrypted parameter. You can't see them (modulo the recent attack), but you do resubmit them.
But that's not the full reasoning token context, just a snapshot of the latent state at the end of it, no?
Have a look at the gemini ones they're pretty small.
Looping back latent state isn't that easy. The hidden data is the entire contents of the KV cache which can be massive. I don't think any provider is trying to loop the KV cache through the client, and neural compressions of the reasoning would be lossy / an advanced technique that is still firmly in the realm of research papers, as I understand.