[FEATURE] Add clipboard copy support for /btw output (C keybinding)

Summary

When /btw (or /by the way) produces output in its overlay, there's currently no easy way to copy that output. This proposes adding copy functionality to the /btw popup, ideally in stages.

Proposed Implementation

Stage 1 (Minimal)

Add a C keybinding in the /btw overlay that copies the full response to the user's clipboard. This mirrors how other keybindings work in the popup (e.g., Esc to dismiss) and would be the simplest path to value.

Stage 2 (Enhanced)

When the user presses C, run the same logic as the /copy slash command rather than a raw clipboard write. This gives:

• Fallback to temp file if clipboard access fails (writes to the session's temp directory)
• Parsed/partial output selection — let the user choose which parts of the /btw response to copy (e.g., just a code block), matching /copy's existing UX

Stage 3 (Larger rework — optional/future)

Temporarily surface the /btw output as if it were the latest assistant message, highlighted in yellow (or another visual indicator) to make it clear this is ephemeral. This would:

• Allow slash commands like /copy to naturally operate on the /btw output
• Disappear on the user's next prompt, restoring the real conversation state

This stage is more invasive and could be a separate effort, but it's the most seamless UX.

Motivation

/btw is great for quick side questions, but the output is trapped in an ephemeral overlay. Users frequently want to save or reuse parts of it (code snippets, explanations, commands). Today the only option is manual text selection, which is clunky in a terminal.

Related Issues

• #37582 — Promoting /btw responses into conversation context (different goal: persistence vs. copying)
• #5512 — General /copy command for main conversation messages (doesn't cover /btw overlay)