feat(shared): replace settle buttons with payment ledger

- New split_payments table records actual payments between participants
- Balance = total split obligations - total payments (splits never marked settled)
- Record Payment modal per participant: direction toggle, amount pre-filled with balance, date, notes
- Payment history inline on each balance card with +/- display and delete
- Per-transaction Settle button removed; Action column removed from shared table
- Splits always show the true cost breakdown regardless of payment state

prisma/migrations/0009_split_payments/migration.sql

@@ -0,0 +1,13 @@
+CREATE TABLE split_payments (
+  id SERIAL PRIMARY KEY,
+  from_participant_id INTEGER NOT NULL REFERENCES participants(id),
+  to_participant_id   INTEGER NOT NULL REFERENCES participants(id),
+  amount              DECIMAL(10,2) NOT NULL CHECK (amount > 0),
+  payment_date        DATE NOT NULL,
+  notes               TEXT,
+  linked_transaction_id INTEGER REFERENCES transactions(id) ON DELETE SET NULL,
+  created_at          TIMESTAMPTZ NOT NULL DEFAULT NOW()
+);
+
+CREATE INDEX idx_split_payments_from ON split_payments(from_participant_id);
+CREATE INDEX idx_split_payments_to   ON split_payments(to_participant_id);

prisma/schema.prisma

@@ -24,6 +24,8 @@ model participants {
   created_at            DateTime                @default(now())
   splits                transaction_splits[]
   account_owner_mappings account_owner_mappings[]
+  payments_sent         split_payments[]         @relation("payments_from")
+  payments_received     split_payments[]         @relation("payments_to")
 }
 
 model account_owner_mappings {
@@ -50,6 +52,19 @@ model transaction_splits {
   @@unique([transaction_id, participant_id])
 }
 
+model split_payments {
+  id                    Int           @id @default(autoincrement())
+  from_participant_id   Int
+  to_participant_id     Int
+  amount                Decimal       @db.Decimal(10, 2)
+  payment_date          DateTime      @db.Date
+  notes                 String?
+  linked_transaction_id Int?
+  created_at            DateTime      @default(now())
+  from_participant      participants  @relation("payments_from", fields: [from_participant_id], references: [id])
+  to_participant        participants  @relation("payments_to", fields: [to_participant_id], references: [id])
+}
+
 model tags {
   id               Int                @id @default(autoincrement())
   name             String             @unique