Sending the whole context on each user message is essentially what the model remembers of this conversation. ie: it is entirely stateless.

I've written some agents that have their context altered by another llm to get it back on track. Let's say the agent is going off rails, then a supervisor agent will spot this and remove messages from the context where it went off rails, or alter those with correct information. Really fun stuff but yeah, we're essentially still inventing this as we go along.