[glitchc]

It's important to realize that the session is jointly owned between the model and the user. Part of the session, such as the reasoning tokens, are generated entirely by the model. Other parts, entirely by the user. However, the ownership and use of all parts is subject to the service provider's terms and conditions, which the user accepts prior to access to the service.

I don't use these models but I am confident the T&Cs establish the service provider's rights in all of the bullets mentioned, from what can be done with the user's prompts to how searches and reasoning contexts are managed. In that sense, it's very similar to cloud services, and we see an overlap between service providers in both sectors.

Ultimately one is buying a service, and all boundaries around what can and cannot be done are defined by the terms and conditions. If portability is a hard requirement, then the best thing to do is to look for services that enshrine portability in their terms.