refactor(backend): quota.measured helper, consistent admin gating, messageable predicate

- quota.measured() context manager folds the before/after units diff that the
  manual sync routes each re-spelled (also makes quota_remaining_today consistent).
- sync pause/resume now use Depends(admin_user) instead of inline role checks.
- is_messageable_user() unifies the 'real, active, non-suspended human' rule that
  was encoded three ways (WS auth, send recipient, and the SQL _messageable()).

backend/app/routes/messages.py

@@ -103,6 +103,7 @@ def _serialize_msg(m: Message) -> dict:
 
 
 def _messageable() -> list:
+    """SQL clauses for "a real, active, non-suspended human" — for directory/recipient queries."""
     return [
         User.is_demo.is_(False),
         User.is_active.is_(True),
@@ -110,6 +111,11 @@ def _messageable() -> list:
     ]
 
 
+def is_messageable_user(u: User | None) -> bool:
+    """Python mirror of `_messageable()` for an already-loaded row (WS auth, send recipient)."""
+    return bool(u and not u.is_demo and u.is_active and not u.is_suspended)
+
+
 def ensure_welcome(db: Session, user: User) -> None:
     """Create the one-time system welcome message for a (human) user the first time it's needed.
     Idempotent: guarded on whether any system message already exists for them."""
@@ -315,7 +321,7 @@ def send_message(
     if payload.recipient_id == user.id:
         raise HTTPException(status_code=400, detail="You can't message yourself.")
     recipient = db.get(User, payload.recipient_id)
-    if recipient is None or recipient.is_demo or not recipient.is_active or recipient.is_suspended:
+    if not is_messageable_user(recipient):
         raise HTTPException(status_code=404, detail="Recipient not available.")
     if db.get(MessageKey, recipient.id) is None:
         raise HTTPException(status_code=404, detail="That member hasn't set up messaging yet.")
@@ -363,8 +369,7 @@ async def messages_ws(ws: WebSocket) -> None:
         return
     db = SessionLocal()
     try:
-        u = db.get(User, uid)
-        ok = bool(u and not u.is_demo and not u.is_suspended and u.is_active)
+        ok = is_messageable_user(db.get(User, uid))
     finally:
         db.close()
     if not ok: