Recognize TaskStop'd bg tasks and harden cross-session liveness

Fix A - TaskStop completion recognition: list_pending_background_task_ids
now treats a TaskStop tool_result (.toolUseResult.message "Successfully
stopped task: <id>") as a terminal completion event, because many Claude
Code builds do not also emit a task_notification system record for a
TaskStop. The id is read from .task_id, falling back to parsing it out of
the message text when that field is absent; the fallback uses
try/catch empty so a degenerate message cannot raise and wipe the whole
completed set under pipefail.

Fix B - cross-session liveness glob: is_bg_task_alive now searches
sibling session dirs under the same project slug when neither the
transcript-recorded output path nor the session-derived path exists.
This only expands where we look, so a genuinely alive task is never
wrongly pruned; a file missing everywhere still fails open as before.

Builds on #215 (extract_bg_task_output_path_from_transcript); the shared
lines drop out of the diff once #215 lands.

Tests: 50/50 (descriptive names, local style).

Author: SwordFaith

hooks/lib/loop-bg-tasks.sh

@@ -183,6 +183,27 @@ is_bg_task_alive() {
     fi
     [[ -n "$output_file" ]] || output_file="$tasks_dir/$task_id.output"
 
+    # Session-resume fallback: when the transcript has no extractable
+    # launch path AND the session-derived path does not exist, the real
+    # .output file likely lives under a DIFFERENT session id (the one that
+    # launched the task). Search sibling session dirs under the same
+    # project slug before giving up. This only EXPANDS where we look, so a
+    # genuinely alive task is never wrongly pruned (its file exists and
+    # lsof still sees the open fd); a file missing everywhere remains
+    # genuinely unknown and fails open below as before.
+    if [[ ! -e "$output_file" ]] && [[ -n "$tasks_dir" ]]; then
+        local slug_dir _candidate
+        slug_dir=$(dirname "$(dirname "$tasks_dir")")   # /tmp/claude-<uid>/<slug>
+        if [[ -d "$slug_dir" ]]; then
+            for _candidate in "$slug_dir"/*/tasks/"$task_id".output; do
+                if [[ -f "$_candidate" ]]; then
+                    output_file="$_candidate"
+                    break
+                fi
+            done
+        fi
+    fi
+
     # Output file absent -> fail open (treat as still running).
     [[ -f "$output_file" ]] || return 0
     # lsof unavailable -> fail open.
@@ -213,7 +234,7 @@ prune_dead_bg_task_ids() {
 #   - Background shell: toolUseResult.backgroundTaskId non-empty
 #     -> id is toolUseResult.backgroundTaskId
 #
-# Completion events are recognised from two Claude Code transcript forms:
+# Completion events are recognised from three Claude Code transcript forms:
 #
 #   1. Structured SDK record
 #      (see SDKTaskNotificationMessage in docs/typescript.md):
@@ -225,6 +246,15 @@ prune_dead_bg_task_ids() {
 #      `<task-notification>` XML block with `<task-id>...</task-id>`;
 #      kept for transcripts produced by older Claude Code versions.
 #
+#   3. TaskStop tool_result: when the model or user stops a background
+#      task via the TaskStop tool, Claude Code records a top-level
+#      `.toolUseResult` whose `.message` is "Successfully stopped task:
+#      <id>" and (usually) whose `.task_id` is the stopped id. The id is
+#      read from `.task_id` when present and otherwise parsed out of the
+#      message text as a fallback. Many builds do NOT also emit a
+#      `task_notification` system event for a TaskStop, so this source is
+#      required or stopped tasks stay pending forever.
+#
 # pending := launched \ completed
 #
 # Optional second argument `since_ts` (ISO-8601 string, e.g. the value
@@ -272,7 +302,7 @@ list_pending_background_task_ids() {
         | (.toolUseResult.agentId // .toolUseResult.backgroundTaskId)
     ' "$transcript_path" 2>/dev/null | sort -u) || return 1
 
-    # Union of both completion formats. Either source alone is enough to
+    # Union of all completion formats. Any one source alone is enough to
     # mark a launched id terminal.
     #
     # The `grep -oE || true` guard on the legacy branch keeps `set -o
@@ -293,6 +323,25 @@ list_pending_background_task_ids() {
             ' "$transcript_path" 2>/dev/null \
                 | { grep -oE '<task-id>[^<]+</task-id>' || true; } \
                 | sed -E 's|</?task-id>||g'
+            # TaskStop tool_result (source 3 above): the model/user stopped
+            # a background task. Match the top-level .toolUseResult whose
+            # .message is "Successfully stopped task: <id>" and emit its id.
+            # Required because many builds do not also emit a task_notification
+            # system event for a TaskStop. The id is read from .task_id when
+            # present; otherwise it is parsed out of the message text as a
+            # fallback, because some builds record the id only there. The
+            # `try ... catch empty` keeps a degenerate message (prefix with
+            # no id, so the regex cannot match) from raising and poisoning
+            # the pipefail pipeline.
+            jq -r '
+                select(.toolUseResult != null)
+                | select((.toolUseResult.message // "")
+                         | contains("Successfully stopped task:"))
+                | (.toolUseResult.task_id
+                   // try ((.toolUseResult.message // "")
+                         | capture("Successfully stopped task: (?<i>[^ (]+)")
+                         | .i) catch empty)
+            ' "$transcript_path" 2>/dev/null
         } | sort -u | sed '/^$/d'
     ) || completed=""