[FEATURE]: Continue /btw side-question threads with follow-ups #52079

Summary

Allow users to continue a /btw side-question thread with follow-up messages.

Today /btw makes a one-shot, ephemeral request. A subsequent /btw starts a separate side question, so it cannot build on the prior /btw question and answer. There is no way to send another user message to the existing side thread.

Expected behavior

Provide a way to submit follow-up questions in the same /btw thread, with prior side-thread messages available as context. Keep that thread isolated from the parent session history unless the user explicitly forks or shares it back.

Starting a new side thread should remain possible, but should not be the only way to ask another question.

Steps to reproduce

1. In a session, ask a question with /btw.
2. Ask a related follow-up with /btw.
3. Observe that the second request starts a separate one-shot side question and cannot use the first side exchange as conversation context.

Related

• [FEATURE]: a /btw answer is unrecoverable once its dialog closes #50879 tracks recovering a /btw answer after its dialog closes. This request is specifically about multi-turn follow-up within the same side thread.