fix(budget): an expense with no payer creates no debt

An expense saved with "No one paid yet" was still charging its split
members in calculateSettlement while crediting nobody, so the ledger
drifted off zero by the unpaid total. The greedy simplifier that turns
balances into payments has no memory of which expense produced which
debt, so it handed that phantom amount to whoever happened to be a
creditor from an unrelated expense. In the report, two people each owed
about 80 to someone who never paid that bill. Booking every payment it
offered then left one member permanently short, next to an "everyone
square" line.

Both cost panels already promise the opposite: they label such a row
"Unfinished, total only, not settled yet" and count it into the
Outstanding amount card instead. The server now agrees with them.

The guard deliberately does not also require a non-zero total, unlike the
panels' label predicate. PUT /budget/:id/payers with an empty array zeroes
total_price without re-applying it, which would otherwise leave a custom
split debiting its members against no credit at all.

The #1543 fixture and BUDGET-SVC-DB-004/005 were re-baselined: they pinned
the old arithmetic through a deliberately payer-less 9 000 RUB item. The
wiki said the old behaviour was intended, so it is updated too.

Closes #2225

server/src/nest/budget/budget.service.ts

@@ -765,6 +765,24 @@ export class BudgetService {
       const payers = allPayers.filter(p => p.budget_item_id === item.id);
       if (members.length === 0) continue; // planning-only entry → doesn't affect balances
 
+      // An expense nobody has paid stays out of the ledger (#2225), which is what
+      // both cost panels already promise by flagging the row "Unfinished" (the
+      // hint beside it reads: total only, not settled yet) and counting it into
+      // the Outstanding card instead (CostsPanel/costsModel.isUnfinished). The
+      // panels additionally require a non-zero total to paint that label; the
+      // ledger deliberately does not, or PUT /budget/:id/payers with an empty
+      // array (which zeroes total_price and does not re-apply it) would leave a
+      // custom split debiting its members against no credit at all.
+      // Charging its split members regardless, as #1382/#2176/#1543 left in
+      // place below, debits a share with no credit behind it: Σ(balances) drifts
+      // off zero by the unpaid total, and the greedy simplifier at the end of this
+      // method has no memory of which expense made which debt, so it pairs the
+      // inflated debtor with a creditor from some unrelated expense and offers a
+      // payment between two people who never shared a bill. Booking every flow it
+      // offered then left someone short: "everyone square" beside a balance that
+      // is not zero.
+      if (!payers.some(p => p.amount !== 0)) continue;
+
       // Payers are credited what they actually paid (converted to trip currency with
       // the item's stored exchange rate). A negative payer — the recipient of a
       // refund (#2176) — is debited by the same arithmetic: their credit is negative.
@@ -781,14 +799,12 @@ export class BudgetService {
       // total_price: the two are the same figure (the write path derives the total
       // from the payer sum), but converting the total separately would round to a
       // different cent on a foreign-currency expense and leave the item off by one.
-      // With nobody down as a payer there is nothing to divide, so the recorded total
-      // stands in and an unpaid bill keeps reading as money owed. Negative credits
-      // (a refund, #2176) divide the same way — only exactly zero falls back.
+      // Negative credits (a refund, #2176) divide the same way. Nothing falls back
+      // to total_price any more: an item with no payer behind it never reaches
+      // here since #2225. An item whose payers net to exactly zero still does, and
+      // divides zero, which is what it is worth.
       const hasCustomSplit = members.some(m => m.amount !== null && m.amount !== undefined);
-      const splitCents = creditCents !== 0
-        ? creditCents
-        : toTripCents(item.total_price, item.currency, item.exchange_rate);
-      const equalShares = !hasCustomSplit ? this.splitEqualShares(splitCents, members, item.id) : {};
+      const equalShares = !hasCustomSplit ? this.splitEqualShares(creditCents, members, item.id) : {};
       for (const m of members) {
         const memberShare = hasCustomSplit && m.amount !== null && m.amount !== undefined
           ? toTripCents(m.amount, item.currency, item.exchange_rate)