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.
There was an attack that convinced models to leak the contents of the reasoning tokens, and it came back as text that matched the length of the encrypted data very well. So it's probably still tokens.
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.
Edit:
I've realised I was incorrect, the thinking doesn't get passed back and forth but the latent snapshot does which result in using memory just the same.