So this means I can not resume a session older than 30 days properly?

I have no idea; you have to check their docs.

AFAIK what they do is that they calculate a hash of the true thinking trace, save it into a database, and only send those hashes back to you (try to man-in-the-middle Claude Code and you'll see those hashes). So then when you send then back your session's history you include those hashes, they look them up in their database, replace them with the real thinking trace, and hand that off to the LLM to continue generation. (All SOTA LLMs nowadays retain reasoning content from previous turns, including Claude.)

I see. If that's just hashes and not encrypted content I can't see how they can resume old sessions properly. IIRC they have a 30 days retention policy and surely the thinking traces must be considered data. Wonder how this works with the zero-retention enterprise plans...

So we are paying the price for the cost of infra need to protect their asset which was trained on data derived from the work of others while ignoring the same principle? I need this to make sense.