feat(daemon): add sync backoff and consolidate hints into tips

Daemon sync improvements:
- Adds exponential backoff on sync failures (30s → 1m → 2m → 5m → 10m → 30m cap)
- Tracks sync state in .beads/sync-state.json (NeedsManualSync, FailureCount, BackoffUntil)
- Resets backoff on daemon start and manual bd sync
- Adds sync-state.json to default .gitignore

Tips consolidation (following ox-cli pattern):
- Moves sync conflict hint from hints.go into tips.go
- Proactive health checks trump educational tips
- Uses InjectTip() with high priority (200) and 100% probability for urgent warnings
- Removes deprecated hints.go

cmd/bd/tips.go

@@ -14,6 +14,7 @@ import (
 	"sync"
 	"time"
 
+	"github.com/steveyegge/beads/internal/beads"
 	"github.com/steveyegge/beads/internal/storage"
 )
 
@@ -353,6 +354,30 @@ func initDefaultTips() {
 			return isClaudeDetected() && !isClaudeSetupComplete()
 		},
 	)
+
+	// Sync conflict tip - ALWAYS show when sync has failed and needs manual intervention
+	// This is a proactive health check that trumps educational tips (ox-cli pattern)
+	InjectTip(
+		"sync_conflict",
+		"Run 'bd sync' to resolve sync conflict",
+		200,         // Higher than Claude setup - sync issues are urgent
+		0,           // No frequency limit - always show when applicable
+		1.0,         // 100% probability - always show when condition is true
+		syncConflictCondition,
+	)
+}
+
+// syncConflictCondition checks if there's a sync conflict that needs manual resolution.
+// This is the condition function for the sync_conflict tip.
+func syncConflictCondition() bool {
+	// Find beads directory to check sync state
+	beadsDir := beads.FindBeadsDir()
+	if beadsDir == "" {
+		return false
+	}
+
+	state := LoadSyncState(beadsDir)
+	return state.NeedsManualSync
 }
 
 // init initializes the tip system with default tips