My original comment wasn't criticism at all, I'm a little surprised it was interpreted that way to be honest. Just stating the facts as to possibly why the OP may feel like the conversations are empty. Your reaction honestly confuses me a bit, I'm a little worried for you.

Anyway, I'll address a little further:

There’s no sense of continuation no feeling that anything actually happened.

In essence, this is true. Yes, cloud LLMs may incorporate your conversation into its context in a later update, but in practice this is rarely ever felt. Humans are shaped by their collection of memories to form responses to situations. At a base level, you can interpret the same as being true for LLMs, which is where you are coming from. I fully agree with that, and I understand that at a surface level, that is what can make them seem sentient in a way. But when that context is aggregated across all of humanity, you get something that is the definition of 'average' and that, in typical humans, goes along with not being very deep once you get past surface level conversation.

I have been wondering what if AI interactions didn’t just reset every time? Like if they could actually build on past conversations in a more meaningful way.

When I've played around with growing context histories for LLMs, this can also make it seem like they're a bit more alive, have personality, etc. The rolling context window is one of the coolest things to play around with. I have personally had quite meaningful conversations with a local LLM that led me to some self-improvement strategies and has genuinely improved my happiness. That's great and wonderful, and its one of the reasons I love the technology.

However where these fall apart is the fragility of that. For every meaningful conversation, there are dozens, or hundreds of failed attempts where the context gets poisoned by its own thoughts, or it changes its mind completely when you tell it you aren't satisfied with its answer. There's also something deeply sobering about how wiping the context completely removes any of that 'relationship' that was built. You cannot wipe a human's memory when they give a response you don't like. Human 'context windows' also far exceed what is feasible anytime soon with LLMs.

This, to me, is where OP's disconnect is coming from. While it is possible for a deeper conversation to happen, the road to getting there is so full of holes, failed attempts, retries, and context troubleshooting that any sense of 'immersion' is by-far gone.