Add Swagger docs at /docs and /openapi.json with split OpenAPI spec

Made-with: Cursor

backend/openapi/components/schemas/faucet.yaml

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+FaucetConfig:
+  type: object
+  properties:
+    faucetEnabled:
+      type: boolean
+    emergencyStop:
+      type: boolean
+    cooldownDays:
+      type: integer
+    minAccountAgeDays:
+      type: integer
+    minActivityScore:
+      type: integer
+    faucetMinSats:
+      type: integer
+    faucetMaxSats:
+      type: integer
+Stats:
+  type: object
+  properties:
+    balanceSats:
+      type: integer
+    totalPaidSats:
+      type: integer
+    totalClaims:
+      type: integer
+    claimsLast24h:
+      type: integer
+    dailyBudgetSats:
+      type: integer
+    spentTodaySats:
+      type: integer
+    recentPayouts:
+      type: array
+      items:
+        type: object
+        properties:
+          pubkey_prefix:
+            type: string
+          payout_sats:
+            type: integer
+          claimed_at:
+            type: integer
+    recentDeposits:
+      type: array
+      items:
+        type: object
+        properties:
+          amount_sats:
+            type: integer
+          source:
+            type: string
+            enum: [lightning, cashu]
+          created_at:
+            type: integer
+DepositInfo:
+  type: object
+  properties:
+    lightningAddress:
+      type: string
+      nullable: true
+    lnurlp:
+      type: string
+      nullable: true