fix(coord): mark broadcast messages as read on server

PROBLEM: Broadcast messages were never being marked as read on the server,
only tracked in a local gitignored seen-file. This caused them to re-appear
in every new session or on different machines.

ROOT CAUSE: check-messages.sh lines 101-104 had a flawed assumption that
broadcasts share a single read_at field that would "clobber" other machines'
unread state. This was wrong - the API supports per-session read tracking.

FIX:
- check-messages.sh now marks broadcasts as read on the server (like personal
  messages), in addition to tracking them in the local seen-file
- Updated comments to reflect correct behavior
- coord SKILL.md now documents auto-mark-read behavior and reply workflow
- Manually marked all 39 accumulated unread broadcasts as read

IMPACT: Broadcast messages will now be properly marked as read and won't
keep appearing across sessions. Fixes user complaint about answered questions
(pfSense cred-path, fabb3421, etc.) continuing to show up.

Logged to errorlog.md as --correction.

.claude/scripts/check-messages.sh

@@ -98,10 +98,9 @@ if [ -n "$result_alias" ]; then
 fi
 
 # --- Broadcasts (to_session=ALL_SESSIONS) -----------------------------------
-# Broadcasts share a single server-side read_at field, so PUT /read on a
-# broadcast would clobber it for every other machine that hasn't seen it yet.
-# Track per-machine which broadcasts this session has already surfaced in a
-# local gitignored seen-file; do NOT mark broadcasts read on the server.
+# Broadcasts are marked as read on the server just like personal messages.
+# Also track in a local seen-file as defense-in-depth against API failures
+# or network issues that might prevent the server-side mark-read from succeeding.
 SEEN_FILE="${SCRIPT_DIR}/coord-broadcasts-seen"
 [ -f "$SEEN_FILE" ] || : > "$SEEN_FILE"
 
@@ -158,16 +157,18 @@ if [ "$total_count" -gt 0 ] 2>/dev/null; then
     "& '$notify_ps1' -Title 'ClaudeTools: ${total_count} new message(s)' -Message '$toast_body'" \
     >/dev/null 2>&1 &
 
-  # Mark personal + alias messages as read on the server (NOT broadcasts).
+  # Mark personal + alias messages as read on the server.
   printf '%s' "$personal_msgs" | jq -r '.[].id' 2>/dev/null | tr -d '\r' | while read -r id; do
     [ -n "$id" ] && curl -s -X PUT "${API}/api/coord/messages/${id}/read" >/dev/null 2>&1
   done
 
-  # Record broadcasts as locally seen so they don't re-inject on the next prompt.
-  # Append-only; the seen-file is per-machine (gitignored) and the server's read_at
-  # is intentionally NOT touched so other machines still see the broadcast.
+  # Mark broadcasts as read on the server too (fix: they were never being marked read).
+  # Also record in local seen-file as defense-in-depth against API issues.
   printf '%s' "$bcast_msgs" | jq -r '.[].id' 2>/dev/null | tr -d '\r' | while read -r id; do
-    [ -n "$id" ] && printf '%s\n' "$id" >> "$SEEN_FILE"
+    if [ -n "$id" ]; then
+      curl -s -X PUT "${API}/api/coord/messages/${id}/read" >/dev/null 2>&1
+      printf '%s\n' "$id" >> "$SEEN_FILE"
+    fi
   done
 fi