Render /side and /btw conversations in a TUI sidecar pane

Feature request

Render CLI /side and /btw conversations in an internal TUI sidecar pane so the parent conversation remains visible while the side conversation is active.

This is a presentation-only request. It is not asking to change /side semantics, persistence, tool permissions, or the existing /side / /btw command surface.

Problem

/side and /btw are useful because they let a user ask a focused side question without polluting the main thread. The current CLI experience still feels disorienting during long-running work because entering a side conversation visually replaces the parent conversation surface. The parent thread still exists, and recent changes already surface parent status, but the parent transcript itself is no longer visible as a working reference.

For users who rely on side conversations while the main thread is busy, this creates a mental-context problem:

• the side conversation is supposed to stay anchored to the parent thread;
• the user often needs to glance at the parent transcript while asking the side question;
• switching into the side conversation makes that visible context disappear;
• the side conversation can then feel like a blank temporary workspace, even though it was created from the parent context.

This is especially painful for users who are forgetful, returning from a long-running turn, or using /side to clarify something while keeping the main task moving.

Proposed behavior

When the CLI enters /side or /btw, show the side conversation in an internal TUI sidecar pane rather than replacing the visible parent conversation.

Suggested layout:

• On wide terminals: parent conversation on the left, side conversation on the right.
• On narrow terminals: parent conversation above, side conversation below.
• Focus moves into the side pane after /side or /btw opens.
• A stable shortcut toggles focus between parent and side panes.
• The UI distinguishes parent busy state from side busy state.
• Existing parent-status surfacing still applies, but it is complemented by visible parent transcript context.

This should be a Codex TUI layout, not host-terminal automation. It should not require tmux, iTerm, terminal tabs, or external split-pane APIs.

Non-goals

Please keep the existing side-conversation semantics:

• Keep /side and /btw as the existing commands.
• Keep side conversations ephemeral unless a separate persistence feature is accepted.
• Keep inherited parent history reference-only.
• Keep existing mutation guardrails: the side conversation should avoid workspace mutations unless the user explicitly asks for them in the side conversation.
• Do not add a new slash command.
• Do not make side conversations durable child threads as part of this request.
• Do not change the side conversation tool-permission model as part of this request.

Why this is separate from related issues

Related work:

• #18125 requested side questions without affecting the main session context.
• #18190 added /side conversations.
• #18591 surfaced parent thread status while in side conversations.
• #23592 added /btw as an alias for /side.
• #26227 requests durable side chats as child threads.
• #28106 requests read-only access from side conversations to current parent-thread state.
• #27179 discusses tightening multi-agent tool boundaries in side conversations.

This request is narrower than #26227 and #28106. It is about the presentation surface: keeping the parent transcript visibly available while the side conversation is active.

Expected outcome

A user can start /side or /btw, continue interacting with the side conversation, and still visually reference the parent thread without exiting side mode. This preserves the lightweight side-conversation workflow while reducing disorientation and context loss in the CLI.