[FEATURE] Side chat (/btw) should know it is a side chat and be able to relay messages back to the main thread

Environment: Claude Code desktop app (Code tab), 2.1.283. I run long multi-agent sessions with ultracode / the Workflow tool, with many background workflows and subagents going at once.

Problem 1: the side chat doesn't know it is a side chat

In the side chat (Cmd/Ctrl+; or /btw), the model acts as if it were the main task. It says things like "before you stopped the task" and reasons as if the main run had been interrupted or handed over to it, when the main agent is still working.

Expected: the side chat knows it is a side conversation. It can read the main thread's state but never assumes ownership of the task and never implies the main run stopped.

Problem 2: no way to relay a side-chat message back to the main thread

After working something out in the side chat, the only way to pass it to the main agent is to re-type it in the main chat. During a workflow run that is costly, because main-chat messages are currently relayed into newly spawned workflow subagents as their governing instruction and can derail them (#95369, #96640, #97076).

Expected (like Codex): an explicit "send to main thread" action. The message is queued for the main agent, clearly marked as coming from the side chat, and never delivered to running subagents.

Why this matters

Until the relay bugs above are fixed, the side chat is the only safe place to ask status questions during an ultracode run. Neither problem is covered by the existing side-chat issues I found, such as #95521 and #96001.