feat(billing): add usage increment API + wire hand/pipeline execution tracking

Server side:
- POST /api/v1/billing/usage/increment endpoint with dimension whitelist
  (hand_executions, pipeline_runs, relay_requests) and count validation (1-100)
- Returns updated usage quota after increment

Desktop side:
- New saas-billing.ts mixin with incrementUsageDimension() and
  reportUsageFireAndForget() (non-blocking, safe for finally blocks)
- handStore.triggerHand: reports hand_executions after successful run
- PipelinesPanel.handleRunComplete: reports pipeline_runs on completion
- SaaSClient type declarations for new billing methods

Billing pipeline now covers all three dimensions:
  relay_requests  → relay handler (server-side, real-time)
  hand_executions → handStore (client-side, fire-and-forget)
  pipeline_runs   → PipelinesPanel (client-side, fire-and-forget)

desktop/src/lib/saas-billing.ts

@@ -0,0 +1,60 @@
+/**
+ * SaaS Billing Methods — Mixin
+ *
+ * Installs billing-related methods (usage increment, quota check) onto
+ * SaaSClient.prototype. Uses the same mixin pattern as saas-telemetry.ts.
+ */
+
+export interface UsageIncrementResult {
+  dimension: string;
+  incremented: number;
+  usage: {
+    relay_requests: number;
+    hand_executions: number;
+    pipeline_runs: number;
+    input_tokens: number;
+    output_tokens: number;
+    [key: string]: unknown;
+  };
+}
+
+export function installBillingMethods(ClientClass: { prototype: any }): void {
+  const proto = ClientClass.prototype;
+
+  /**
+   * Report a usage increment for a specific dimension.
+   *
+   * Called after hand execution, pipeline run, or other metered operations.
+   * Non-blocking — failures are logged but don't affect the caller.
+   *
+   * @param dimension - One of: hand_executions, pipeline_runs, relay_requests
+   * @param count - How many units to increment (default 1, max 100)
+   */
+  proto.incrementUsageDimension = async function (
+    this: { request<T>(method: string, path: string, body?: unknown): Promise<T> },
+    dimension: string,
+    count: number = 1,
+  ): Promise<UsageIncrementResult> {
+    return this.request<UsageIncrementResult>(
+      'POST',
+      '/api/v1/billing/usage/increment',
+      { dimension, count },
+    );
+  };
+
+  /**
+   * Fire-and-forget version of incrementUsageDimension.
+   * Logs errors but never throws — safe to call in finally blocks.
+   */
+  proto.reportUsageFireAndForget = function (
+    this: { incrementUsageDimension(dimension: string, count?: number): Promise<UsageIncrementResult> },
+    dimension: string,
+    count: number = 1,
+  ): void {
+    this.incrementUsageDimension(dimension, count).catch((err: unknown) => {
+      // Non-fatal: billing reporting failure must never block user operations
+      const msg = err instanceof Error ? err.message : String(err);
+      console.warn(`[Billing] Failed to report ${dimension} usage (+${count}): ${msg}`);
+    });
+  };
+}

desktop/src/lib/saas-client.ts

@@ -132,6 +132,7 @@ import { installAdminMethods } from './saas-admin';
 import { installRelayMethods } from './saas-relay';
 import { installPromptMethods } from './saas-prompt';
 import { installTelemetryMethods } from './saas-telemetry';
+import { installBillingMethods } from './saas-billing';
 
 // === Client Implementation ===
 
@@ -411,6 +412,7 @@ installAdminMethods(SaaSClient);
 installRelayMethods(SaaSClient);
 installPromptMethods(SaaSClient);
 installTelemetryMethods(SaaSClient);
+installBillingMethods(SaaSClient);
 
 // === API Method Type Declarations ===
 // These methods are installed at runtime by installXxxMethods() in saas-*.ts.
@@ -516,6 +518,10 @@ export interface SaaSClient {
       timestamp: string;
     }>;
   }): Promise<{ accepted: number; total: number }>;
+
+  // --- Billing (saas-billing.ts) ---
+  incrementUsageDimension(dimension: string, count?: number): Promise<import('./saas-billing').UsageIncrementResult>;
+  reportUsageFireAndForget(dimension: string, count?: number): void;
 }
 
 // === Singleton ===