BTW mode has no memory/context persistence between messages

Problem

BTW (background) mode trades context persistence for non-interruption, but this is often a bad trade. When a question is important enough to ask in BTW mode, the answer is probably important enough to remember — but it doesn't stick. Each BTW message starts fresh with no knowledge of prior BTW exchanges.

The "doesn't interrupt" benefit evaporates when you have to re-explain context every time or can't trust that the AI remembers anything you told it.

Expected behavior

BTW mode should retain context/memory across messages, or at minimum there should be a mode that is both non-interrupting AND context-aware.

Current behavior

Each BTW message is stateless. No memory of prior BTW exchanges. Makes it unreliable for anything beyond a one-shot question.