Add logout functionality and Garmin sync structured logging

- Add POST /api/auth/logout endpoint with tests (5 tests)
- Add logout button to settings page (5 tests)
- Add structured logging to garmin-sync cron (sync start/complete/failure)
- Update IMPLEMENTATION_PLAN.md with spec gap analysis findings
- Total: 835 tests passing across 44 test files

Closes spec gaps from authentication.md (logout) and observability.md (logging)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

src/app/api/cron/garmin-sync/route.ts

@@ -13,6 +13,7 @@ import {
   fetchIntensityMinutes,
   isTokenExpired,
 } from "@/lib/garmin";
+import { logger } from "@/lib/logger";
 import {
   activeUsersGauge,
   garminSyncDuration,
@@ -59,6 +60,8 @@ export async function POST(request: Request) {
   const today = new Date().toISOString().split("T")[0];
 
   for (const user of users) {
+    const userSyncStartTime = Date.now();
+
     try {
       // Check if tokens are expired
       const tokens: GarminTokens = {
@@ -72,6 +75,9 @@ export async function POST(request: Request) {
         continue;
       }
 
+      // Log sync start
+      logger.info({ userId: user.id }, "Garmin sync start");
+
       // Check for token expiration warnings (exactly 14 or 7 days)
       const daysRemaining = daysUntilExpiry(tokens);
       if (daysRemaining === 14 || daysRemaining === 7) {
@@ -135,9 +141,26 @@ export async function POST(request: Request) {
         notificationSentAt: null,
       });
 
+      // Log sync complete with metrics
+      const userSyncDuration = Date.now() - userSyncStartTime;
+      logger.info(
+        {
+          userId: user.id,
+          duration_ms: userSyncDuration,
+          metrics: {
+            bodyBattery: bodyBattery.current,
+            hrvStatus,
+          },
+        },
+        "Garmin sync complete",
+      );
+
       result.usersProcessed++;
       garminSyncTotal.inc({ status: "success" });
-    } catch {
+    } catch (error) {
+      // Log sync failure
+      logger.error({ userId: user.id, err: error }, "Garmin sync failure");
+
       result.errors++;
       garminSyncTotal.inc({ status: "failure" });
     }