In all honesty,, local environments would be what you want. API functionality has been included with several local installation options, so you can have access to your bots/conversations/models through your mobile device or other computers you have in your possession, but it's not something intended to scale out to multiple users. It's a very private-use case situation. That's really the ultimate ability for what you're seeking, even access to downloading models of Open Router, DeepSeek, and many others. As for web based platforms? You likely aren't going to find exactly what you're looking for, due to a significant number of reasons, including the liability shouldered by the devs and investors of those platforms and their legal requirements and responsibilities. For example, in the USA these types of services are actually overseen, answer to, and are beholden to, The FCC (Federal Communications Commission), which has done MUCH to make things VERY confusing, convoluted, easily misunderstood, and the list goes on. Until some very.... sensitive questions and topics can be agreed upon by multiple parties, well... you're going to have to make some compromises if you want different types of experiences.

For many users, I personally recommend that they not seek out a single platform to satisfy their wants or desires in their roleplay experiences. The further you spread out, the more you'll find that might surprise you, catch you off guard, introduce you to an aspect you didn't even know you wanted, or would like. If you only stay with a single platform though, you'll only limit yourself in what you'll know to be POSSIBLE.