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/lib/queries.ts

@@ -753,7 +753,7 @@ export interface TripAnalytics {
   daily_spend: { date: string; amount: number }[];
   top_merchants: { merchant: string; amount: number; count: number }[];
   tag_breakdown: { tag_id: number; name: string; color: string; amount: number; count: number }[];
-  participant_splits: { participant_id: number; name: string; owed: number; settled: number; unsettled: number }[];
+  participant_splits: { participant_id: number; name: string; owed: number }[];
 }
 
 export async function getTrips(ownerId: number): Promise<TripRow[]> {
@@ -857,13 +857,19 @@ export async function getTripAnalytics(tripId: number, ownerId: number): Promise
       ORDER BY 4 DESC
     `, [tripId]),
 
-    queryRaw<{ participant_id: number; name: string; owed: number; settled: number; unsettled: number }>(`
+    // No settled/unsettled breakdown here. It was computed from
+    // transaction_splits.settled, which only /api/splits/settle writes and
+    // nothing in the UI calls — so it is false on all 673 splits and every trip
+    // reported 100% unsettled, including trips paid in full. A real per-trip
+    // figure is not computable either: split_payments carries no trip
+    // attribution, so a payment cannot be assigned to a trip. Settlement is a
+    // property of the whole relationship until settlement contexts exist
+    // (see docs/shared-expenses-design.md).
+    queryRaw<{ participant_id: number; name: string; owed: number }>(`
       SELECT
         p.id AS participant_id,
         p.name,
-        SUM(ts.share_percent / 100.0 * COALESCE(tx.amount_aud, tx.amount))::float AS owed,
-        SUM(CASE WHEN ts.settled THEN ts.share_percent / 100.0 * COALESCE(tx.amount_aud, tx.amount) ELSE 0 END)::float AS settled,
-        SUM(CASE WHEN NOT ts.settled THEN ts.share_percent / 100.0 * COALESCE(tx.amount_aud, tx.amount) ELSE 0 END)::float AS unsettled
+        SUM(ts.share_percent / 100.0 * COALESCE(tx.amount_aud, tx.amount))::float AS owed
       FROM transaction_overrides o
       JOIN transactions tx ON tx.id = o.transaction_id
       JOIN transaction_splits ts ON ts.transaction_id = tx.id