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/.env.example

@@ -18,16 +18,9 @@ NONCE_TTL_SECONDS=600
 # Faucet economics
 FAUCET_ENABLED=true
 EMERGENCY_STOP=false
+# Payout: random amount between FAUCET_MIN_SATS and FAUCET_MAX_SATS (inclusive)
 FAUCET_MIN_SATS=10
 FAUCET_MAX_SATS=100
-PAYOUT_WEIGHT_SMALL=50
-PAYOUT_WEIGHT_MEDIUM=30
-PAYOUT_WEIGHT_LARGE=15
-PAYOUT_WEIGHT_JACKPOT=5
-PAYOUT_SMALL_SATS=10
-PAYOUT_MEDIUM_SATS=25
-PAYOUT_LARGE_SATS=50
-PAYOUT_JACKPOT_SATS=100
 DAILY_BUDGET_SATS=10000
 MAX_CLAIMS_PER_DAY=100
 MIN_WALLET_BALANCE_SATS=1000