docs(agent): clarify claude oauth env

scripts/demo-record.sh

@@ -11,8 +11,8 @@ if ! command -v vhs >/dev/null 2>&1; then
   exit 1
 fi
 
-if [ -z "${BOT_BOTTLE_OAUTH_TOKEN:-}" ]; then
-  echo "demo-record: BOT_BOTTLE_OAUTH_TOKEN is unset; claude inside the bottle will not auth" >&2
+if [ -z "${BOT_BOTTLE_CLAUDE_OAUTH_TOKEN:-}" ]; then
+  echo "demo-record: BOT_BOTTLE_CLAUDE_OAUTH_TOKEN is unset; claude inside the bottle will not auth" >&2
   exit 1
 fi
 

scripts/demo.sh

@@ -14,9 +14,9 @@ set -euo pipefail
 
 cd "$(dirname "$0")/.."
 
-if [ -z "${BOT_BOTTLE_OAUTH_TOKEN:-}" ]; then
+if [ -z "${BOT_BOTTLE_CLAUDE_OAUTH_TOKEN:-}" ]; then
   cat <<'EOF' >&2
-demo: BOT_BOTTLE_OAUTH_TOKEN is unset. The bottle launches claude,
+demo: BOT_BOTTLE_CLAUDE_OAUTH_TOKEN is unset. The bottle launches claude,
 which needs the token to authenticate. Set it in your shell env (e.g.
 ~/.zshrc) — see README §Auth — then re-run.
 EOF