Redesign faucet claim flow: login → loading → eligibility → claim

- Backend: payout is now random between FAUCET_MIN_SATS and FAUCET_MAX_SATS
- Remove weighted buckets; simplify config and .env.example
- Frontend: show loading and eligibility in main body, modal only for confirm/success
- Rename Confirm payout to Claim; add styles for body loading and eligible state

Made-with: Cursor

backend/src/services/quote.ts

@@ -6,42 +6,17 @@ import { getWalletBalanceSats } from "./lnbits.js";
 
 const QUOTE_TTL_SECONDS = 60;
 
-interface PayoutBucket {
-  sats: number;
-  weight: number;
-}
-
-function getPayoutBuckets(): PayoutBucket[] {
-  return [
-    { sats: config.payoutSmallSats, weight: config.payoutWeightSmall },
-    { sats: config.payoutMediumSats, weight: config.payoutWeightMedium },
-    { sats: config.payoutLargeSats, weight: config.payoutWeightLarge },
-    { sats: config.payoutJackpotSats, weight: config.payoutWeightJackpot },
-  ];
-}
-
 /**
- * Weighted random selection. Returns sats amount.
- */
-export function selectWeightedPayout(): number {
-  const buckets = getPayoutBuckets();
-  const totalWeight = buckets.reduce((s, b) => s + b.weight, 0);
-  let r = randomInt(0, totalWeight);
-  for (const b of buckets) {
-    if (r < b.weight) return b.sats;
-    r -= b.weight;
-  }
-  return config.payoutSmallSats;
-}
-
-/**
- * Compute payout for this claim: weighted selection, capped by daily budget remaining.
+ * Random payout between FAUCET_MIN_SATS and FAUCET_MAX_SATS (inclusive),
+ * capped by daily budget remaining.
  */
 export function computePayoutForClaim(todayPaidSats: number): number {
   const remaining = Math.max(0, config.dailyBudgetSats - todayPaidSats);
   if (remaining < config.faucetMinSats) return 0;
-  const selected = selectWeightedPayout();
-  return Math.min(selected, remaining, config.faucetMaxSats);
+  const min = Math.max(config.faucetMinSats, 1);
+  const max = Math.min(config.faucetMaxSats, remaining);
+  if (max < min) return 0;
+  return randomInt(min, max + 1);
 }
 
 export interface CreateQuoteResult {