Make btw side questions interactive and toolless

Run /btw through a transient app-server side question instead of reusing the heavier /side thread flow. The TUI now opens a live pager overlay that shows progress and streamed answer text while core enforces a no-tools internal session source for the side question.

Verification: just write-app-server-schema; cargo test -p codex-tui --lib btw_notifications_collect_answer_and_emit_completion; cargo test -p codex-app-server-protocol; just fmt; just fix -p codex-tui

Author: LEON-gittech