fix(received-invoices): treat amount as gross (VAT-inclusive), back-calc VAT

The amount on a received invoice is the GROSS total the user pays (VAT
included), and VAT is the portion contained within it — not a net base with
VAT added on top. Switch the formula from amount*rate/100 to the
VAT-inclusive amount*rate/(100+rate) via a shared, tested vatFromGross()
helper used by both the create (manual upload + AI import share this
endpoint) and edit paths. Rate 0 → no VAT.

- AI extraction now asks Claude for the total INCLUDING VAT (was "základ bez
  DPH"), reinforced in the structured-output schema description.
- Label the amount field "Částka s DPH" in the AI review card and the manual
  upload/edit forms so the gross convention is explicit.
- Add unit tests with the user-confirmed figures (22 542,91 @ 21% → 3 912,41,
  base 18 630,50) plus other rates and the no-VAT case.

Existing rows keep their stored (gross) amounts; their vat_amount recomputes
on next edit. A one-shot backfill can correct historical vat_amount if wanted.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

src/routes/admin/received-invoices.ts

@@ -22,6 +22,15 @@ const VALID_STATUSES = ["unpaid", "paid"] as const;
 function roundMoney(n: number): number {
   return Math.round(n * 100) / 100;
 }
+
+/**
+ * VAT contained WITHIN a gross (VAT-inclusive) amount. `amount` is the total to
+ * pay including tax, so the tax portion is gross * rate / (100 + rate) — e.g.
+ * 22542.91 @ 21% → 3912.41 (base 18630.50). Returns 0 when there is no VAT.
+ */
+export function vatFromGross(gross: number, rate: number): number {
+  return rate > 0 ? roundMoney((gross * rate) / (100 + rate)) : 0;
+}
 const ALLOWED_SORT_FIELDS = [
   "id",
   "supplier_name",
@@ -284,11 +293,8 @@ export default async function receivedInvoicesRoutes(
           const meta = invoicesMeta[i] || {};
           const amount = Number(meta.amount ?? 0);
           const vatRate = Number(meta.vat_rate ?? 21);
-          // Amount is net — VAT = amount * rate / 100
-          const vatAmount =
-            vatRate > 0
-              ? Math.round(((amount * vatRate) / 100) * 100) / 100
-              : 0;
+          // `amount` is the GROSS total (VAT included); VAT is the portion within it.
+          const vatAmount = vatFromGross(amount, vatRate);
 
           const issueDate = meta.issue_date
             ? new Date(String(meta.issue_date))
@@ -448,7 +454,7 @@ export default async function receivedInvoicesRoutes(
         }
       }
 
-      // Recalculate vat_amount when amount or vat_rate changes (matching PHP)
+      // Recalculate vat_amount when amount (gross) or vat_rate changes.
       const finalAmount =
         body.amount !== undefined
           ? Number(body.amount)
@@ -457,9 +463,8 @@ export default async function receivedInvoicesRoutes(
         body.vat_rate !== undefined
           ? Number(body.vat_rate)
           : Number(existing.vat_rate);
-      // Amount is net — VAT = amount * rate / 100
-      const computedVat =
-        finalVatRate > 0 ? roundMoney((finalAmount * finalVatRate) / 100) : 0;
+      // `amount` is the GROSS total (VAT included); VAT is the portion within it.
+      const computedVat = vatFromGross(finalAmount, finalVatRate);
 
       // Auto-set paid_date when status transitions to paid (matching PHP)
       const newStatus =