fix(trips): stop reporting a settlement breakdown that cannot be computed

The trip view showed Total Owed / Settled / Unsettled per participant, with the
last two derived from transaction_splits.settled. Nothing sets that flag - its
only writer was /api/splits/settle, which no UI calls - so it is false on all 673
splits and every trip reported 100% unsettled, including trips already paid in
full. Molina has paid $20,782.79 against $19,556.07 of splits and the Europe trip
still showed her entire share outstanding.

A correct per-trip figure is not computable either: split_payments records only
from, to, amount and date, so a payment cannot be attributed to a trip. The trip
view now shows each participant's share and points at Shared for what is actually
owed, which is where settlement genuinely lives.

Also removes /api/splits/settle. It was unreachable from the UI but live on its
URL, and a single call with participant_id would mark every one of that person's
splits settled - writing a flag nothing reads. Settlement will be reintroduced
against settlement contexts (docs/shared-expenses-design.md).

getParticipantBalances is deliberately untouched: it computes splits minus
payments, which is coherent. Excluding settled splits there while still
subtracting the payments that settled them would double-count.

src/app/api/splits/settle/route.ts

@@ -1,46 +0,0 @@
-import { NextRequest, NextResponse } from "next/server";
-import { queryRaw } from "@/lib/db";
-import { getCurrentUser } from "@/lib/auth";
-
-// A split may be settled by the transaction's effective owner or by the
-// participant the split belongs to.
-const SCOPE = `
-  AND EXISTS (
-    SELECT 1 FROM transactions t
-    LEFT JOIN statements s ON s.id = t.statement_id
-    WHERE t.id = transaction_splits.transaction_id
-      AND (COALESCE(t.owner_id, s.owner_id) = $2 OR transaction_splits.participant_id = $2)
-  )`;
-
-export async function POST(req: NextRequest) {
-  const user = await getCurrentUser(req);
-  if (!user) return NextResponse.json({ error: "Unauthorized" }, { status: 403 });
-
-  const body = await req.json();
-  const { participant_id, split_ids } = body as {
-    participant_id?: number;
-    split_ids?: number[];
-  };
-
-  if (participant_id) {
-    const rows = await queryRaw<{ id: number }>(
-      `UPDATE transaction_splits SET settled = true, settled_at = NOW()
-       WHERE participant_id = $1 AND settled = false ${SCOPE}
-       RETURNING id`,
-      [participant_id, user.id]
-    );
-    return NextResponse.json({ settled: rows.length });
-  }
-
-  if (split_ids?.length) {
-    const rows = await queryRaw<{ id: number }>(
-      `UPDATE transaction_splits SET settled = true, settled_at = NOW()
-       WHERE id = ANY($1::int[]) AND settled = false ${SCOPE}
-       RETURNING id`,
-      [split_ids, user.id]
-    );
-    return NextResponse.json({ settled: rows.length });
-  }
-
-  return NextResponse.json({ error: "participant_id or split_ids required" }, { status: 400 });
-}

src/app/trips/[id]/page.tsx

@@ -277,7 +277,7 @@ export default function TripDetailPage({ params }: { params: Promise<{ id: strin
               <table className="w-full text-sm">
                 <thead>
                   <tr className="border-b border-zinc-800">
-                    {["Person", "Total Owed", "Settled", "Unsettled"].map((h) => (
+                    {["Person", "Share of this trip"].map((h) => (
                       <th
                         key={h}
                         className={`px-5 py-2.5 text-xs text-zinc-500 font-medium ${h === "Person" ? "text-left" : "text-right"}`}
@@ -292,14 +292,20 @@ export default function TripDetailPage({ params }: { params: Promise<{ id: strin
                     <tr key={p.participant_id} className="border-b border-zinc-800/50 last:border-0">
                       <td className="px-5 py-3 font-medium">{p.name}</td>
                       <td className="px-5 py-3 text-right tabular-nums font-mono">${Number(p.owed).toFixed(2)}</td>
-                      <td className="px-5 py-3 text-right tabular-nums font-mono text-emerald-500">${Number(p.settled).toFixed(2)}</td>
-                      <td className={`px-5 py-3 text-right tabular-nums font-mono ${p.unsettled > 0 ? "text-amber-400" : "text-zinc-600"}`}>
-                        ${Number(p.unsettled).toFixed(2)}
-                      </td>
                     </tr>
                   ))}
                 </tbody>
               </table>
+              {/* Settled/unsettled was reported from transaction_splits.settled,
+                  which nothing sets — so every trip showed 100% unsettled forever,
+                  including ones already paid in full. Settlement is tracked across
+                  the whole relationship, not per trip: payments carry no trip
+                  attribution, so a per-trip figure cannot be computed. */}
+              <p className="px-5 py-2.5 text-xs text-zinc-500 border-t border-zinc-800">
+                Settlement is tracked across all shared expenses, not per trip —
+                see <Link href="/shared" className="text-zinc-400 hover:text-zinc-200 underline">Shared</Link> for
+                what is actually owed.
+              </p>
             </div>
           )}