feat(amethyst): show onchain balance on wallet screen Bitcoin section

OnchainSection now fetches UTXOs for the derived Taproot address from the
configured Esplora backend and displays the sum as the section balance.
Loading / unavailable / error states are surfaced inline. No retry on
failure — the user refreshes by re-entering the screen.

Balance fetch runs in a LaunchedEffect keyed on the derived address (which
is keyed on the account pubkey), so it kicks off once per account view.

amethyst/src/main/java/com/vitorpamplona/amethyst/ui/screen/loggedIn/wallet/OnchainSection.kt

@@ -31,18 +31,26 @@ import androidx.compose.material3.MaterialTheme
 import androidx.compose.material3.OutlinedButton
 import androidx.compose.material3.Text
 import androidx.compose.runtime.Composable
+import androidx.compose.runtime.LaunchedEffect
+import androidx.compose.runtime.getValue
+import androidx.compose.runtime.mutableStateOf
 import androidx.compose.runtime.remember
 import androidx.compose.runtime.rememberCoroutineScope
+import androidx.compose.runtime.setValue
 import androidx.compose.ui.Alignment
 import androidx.compose.ui.Modifier
 import androidx.compose.ui.platform.LocalClipboard
 import androidx.compose.ui.text.font.FontWeight
 import androidx.compose.ui.text.style.TextOverflow
 import androidx.compose.ui.unit.dp
+import com.vitorpamplona.amethyst.model.LocalCache
 import com.vitorpamplona.amethyst.ui.components.util.setText
 import com.vitorpamplona.amethyst.ui.screen.loggedIn.AccountViewModel
 import com.vitorpamplona.quartz.nipBCOnchainZaps.taproot.TaprootAddress
+import kotlinx.coroutines.Dispatchers
 import kotlinx.coroutines.launch
+import kotlinx.coroutines.withContext
+import java.text.NumberFormat
 
 /**
  * "Bitcoin" section card on the wallet screen, shown above the lightning NWC
@@ -67,6 +75,32 @@ fun OnchainSection(
             runCatching { TaprootAddress.fromPubKey(pubKey) }.getOrNull()
         }
 
+    // Balance fetched from the configured OnchainBackend. null = unknown / loading
+    // / unconfigured. We intentionally do not retry on failure here — the user can
+    // refresh by leaving and re-entering the screen.
+    var balanceSats by remember(pubKey) { mutableStateOf<Long?>(null) }
+    var balanceState by remember(pubKey) { mutableStateOf(BalanceState.LOADING) }
+
+    LaunchedEffect(address) {
+        if (address == null) {
+            balanceState = BalanceState.UNAVAILABLE
+            return@LaunchedEffect
+        }
+        val backend = LocalCache.onchainBackend
+        if (backend == null) {
+            balanceState = BalanceState.UNAVAILABLE
+            return@LaunchedEffect
+        }
+        balanceState = BalanceState.LOADING
+        try {
+            val utxos = withContext(Dispatchers.IO) { backend.getUtxosForAddress(address) }
+            balanceSats = utxos.sumOf { it.valueSats }
+            balanceState = BalanceState.READY
+        } catch (t: Throwable) {
+            balanceState = BalanceState.ERROR
+        }
+    }
+
     Card(
         modifier = modifier.fillMaxWidth(),
         elevation = CardDefaults.cardElevation(defaultElevation = 1.dp),
@@ -87,6 +121,7 @@ fun OnchainSection(
                     color = MaterialTheme.colorScheme.onSurfaceVariant,
                 )
             } else {
+                BalanceRow(state = balanceState, sats = balanceSats)
                 Text(
                     text = "Your Taproot address",
                     style = MaterialTheme.typography.labelMedium,
@@ -104,6 +139,39 @@ fun OnchainSection(
     }
 }
 
+private enum class BalanceState { LOADING, READY, ERROR, UNAVAILABLE }
+
+@Composable
+private fun BalanceRow(
+    state: BalanceState,
+    sats: Long?,
+) {
+    val text =
+        when (state) {
+            BalanceState.LOADING -> {
+                "Loading balance…"
+            }
+
+            BalanceState.READY -> {
+                val formatted = NumberFormat.getNumberInstance().format(sats ?: 0L)
+                "$formatted sats"
+            }
+
+            BalanceState.ERROR -> {
+                "Balance unavailable"
+            }
+
+            BalanceState.UNAVAILABLE -> {
+                "Chain backend not configured"
+            }
+        }
+    Text(
+        text = text,
+        style = MaterialTheme.typography.headlineSmall,
+        fontWeight = FontWeight.SemiBold,
+    )
+}
+
 @Composable
 private fun CopyAddressRow(address: String) {
     val clipboard = LocalClipboard.current