fix(splits): editing a split must not resurrect a settled debt

The route replaces every split for a transaction rather than editing in place,
so the recreated rows took the column default settled=false. Opening the split
modal on a historical transaction and saving it therefore converted a
discharged obligation into a live one, with nothing on screen saying so.

That is not theoretical. 657 pre-2026 transactions now carry settled splits
imported from SplitMyExpenses -- $37,233.28 of balance that the carryover
(transaction 2348) already accounts for. Editing one would double-count its
share against a debt that was paid years ago.

Now carries settled and settled_at across the rewrite, per participant, the
same way the rules revert route already does. Changing someone's percentage
does not re-open the obligation: it was settled outside this app and stays
settled. A participant who was not on the transaction before is a genuinely new
obligation and correctly starts unsettled.

rule-actions.ts was already safe here -- it upserts ON CONFLICT DO UPDATE SET
share_percent, so it never touches the flag.

src/app/api/transactions/[id]/splits/route.ts

@@ -66,18 +66,47 @@ export async function POST(
     );
   }
 
+  // Carry `settled` across the rewrite.
+  //
+  // This replaces every split rather than editing in place, so without this the
+  // recreated rows take the column default of false — silently converting a
+  // discharged historical obligation into a live debt. That is not theoretical:
+  // 657 pre-2026 transactions carry settled splits imported from
+  // SplitMyExpenses, $37,233.28 of balance that the carryover (transaction
+  // 2348) already accounts for. Editing one would double-count its share, and
+  // nothing on screen would say so.
+  //
+  // Changing someone's percentage does not re-open the obligation — it was
+  // settled outside this app and stays settled. A participant added who was not
+  // there before is a genuinely new obligation and correctly starts unsettled.
+  const previous = await queryRaw<{
+    participant_id: number;
+    settled: boolean;
+    settled_at: string | null;
+  }>(
+    `SELECT participant_id, settled, settled_at
+       FROM transaction_splits WHERE transaction_id = $1`,
+    [transactionId]
+  );
+  const settledBefore = new Map(
+    previous.map((p) => [p.participant_id, { settled: p.settled, settled_at: p.settled_at }])
+  );
+
   // Replace all splits for this transaction atomically
   await prisma.$transaction([
     prisma.transaction_splits.deleteMany({ where: { transaction_id: transactionId } }),
-    ...splits.map((s) =>
-      prisma.transaction_splits.create({
+    ...splits.map((s) => {
+      const before = settledBefore.get(s.participant_id);
+      return prisma.transaction_splits.create({
         data: {
           transaction_id: transactionId,
           participant_id: s.participant_id,
           share_percent: s.share_percent,
+          settled: before?.settled ?? false,
+          settled_at: before?.settled_at ? new Date(before.settled_at) : null,
         },
-      })
-    ),
+      });
+    }),
   ]);
 
   const result = await queryRaw<SplitRow>(