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/daemon_sync_state.go

@@ -0,0 +1,165 @@
+package main
+
+import (
+	"encoding/json"
+	"os"
+	"path/filepath"
+	"sync"
+	"time"
+)
+
+// SyncState tracks daemon sync health for backoff and user hints.
+// Stored in .beads/sync-state.json (gitignored, local-only).
+type SyncState struct {
+	LastFailure     time.Time `json:"last_failure,omitempty"`
+	FailureCount    int       `json:"failure_count"`
+	BackoffUntil    time.Time `json:"backoff_until,omitempty"`
+	NeedsManualSync bool      `json:"needs_manual_sync"`
+	FailureReason   string    `json:"failure_reason,omitempty"`
+}
+
+const (
+	syncStateFile = "sync-state.json"
+	// Backoff schedule: 30s, 1m, 2m, 5m, 10m, 30m (cap)
+	maxBackoffDuration = 30 * time.Minute
+	// Clear stale state after 24 hours
+	staleStateThreshold = 24 * time.Hour
+)
+
+var (
+	// backoffSchedule defines the exponential backoff durations
+	backoffSchedule = []time.Duration{
+		30 * time.Second,
+		1 * time.Minute,
+		2 * time.Minute,
+		5 * time.Minute,
+		10 * time.Minute,
+		30 * time.Minute,
+	}
+	// syncStateMu protects concurrent access to sync state file
+	syncStateMu sync.Mutex
+)
+
+// LoadSyncState loads the sync state from .beads/sync-state.json.
+// Returns empty state if file doesn't exist or is stale.
+func LoadSyncState(beadsDir string) SyncState {
+	syncStateMu.Lock()
+	defer syncStateMu.Unlock()
+
+	statePath := filepath.Join(beadsDir, syncStateFile)
+	data, err := os.ReadFile(statePath) // #nosec G304 - path constructed from beadsDir
+	if err != nil {
+		return SyncState{}
+	}
+
+	var state SyncState
+	if err := json.Unmarshal(data, &state); err != nil {
+		return SyncState{}
+	}
+
+	// Clear stale state (older than 24h with no recent failures)
+	if !state.LastFailure.IsZero() && time.Since(state.LastFailure) > staleStateThreshold {
+		_ = os.Remove(statePath)
+		return SyncState{}
+	}
+
+	return state
+}
+
+// SaveSyncState saves the sync state to .beads/sync-state.json.
+func SaveSyncState(beadsDir string, state SyncState) error {
+	syncStateMu.Lock()
+	defer syncStateMu.Unlock()
+
+	statePath := filepath.Join(beadsDir, syncStateFile)
+
+	// If state is empty/reset, remove the file
+	if state.FailureCount == 0 && !state.NeedsManualSync {
+		_ = os.Remove(statePath)
+		return nil
+	}
+
+	data, err := json.MarshalIndent(state, "", "  ")
+	if err != nil {
+		return err
+	}
+
+	return os.WriteFile(statePath, data, 0600)
+}
+
+// ClearSyncState removes the sync state file.
+func ClearSyncState(beadsDir string) error {
+	syncStateMu.Lock()
+	defer syncStateMu.Unlock()
+
+	statePath := filepath.Join(beadsDir, syncStateFile)
+	err := os.Remove(statePath)
+	if os.IsNotExist(err) {
+		return nil
+	}
+	return err
+}
+
+// RecordSyncFailure updates the sync state after a failure.
+// Returns the duration until next retry.
+func RecordSyncFailure(beadsDir string, reason string) time.Duration {
+	state := LoadSyncState(beadsDir)
+
+	state.LastFailure = time.Now()
+	state.FailureCount++
+	state.FailureReason = reason
+
+	// Calculate backoff duration
+	backoffIndex := state.FailureCount - 1
+	if backoffIndex >= len(backoffSchedule) {
+		backoffIndex = len(backoffSchedule) - 1
+	}
+	backoff := backoffSchedule[backoffIndex]
+
+	state.BackoffUntil = time.Now().Add(backoff)
+
+	// Mark as needing manual sync after 3 failures (likely a conflict)
+	if state.FailureCount >= 3 {
+		state.NeedsManualSync = true
+	}
+
+	_ = SaveSyncState(beadsDir, state)
+	return backoff
+}
+
+// RecordSyncSuccess clears the sync state after a successful sync.
+func RecordSyncSuccess(beadsDir string) {
+	_ = ClearSyncState(beadsDir)
+}
+
+// ShouldSkipSync returns true if we're still in the backoff period.
+func ShouldSkipSync(beadsDir string) bool {
+	state := LoadSyncState(beadsDir)
+	if state.BackoffUntil.IsZero() {
+		return false
+	}
+	return time.Now().Before(state.BackoffUntil)
+}
+
+// ResetBackoffOnDaemonStart resets backoff counters when daemon starts,
+// but preserves NeedsManualSync flag so hints still show.
+// This allows a fresh start while keeping user informed of conflicts.
+func ResetBackoffOnDaemonStart(beadsDir string) {
+	state := LoadSyncState(beadsDir)
+
+	// Nothing to reset
+	if state.FailureCount == 0 && !state.NeedsManualSync {
+		return
+	}
+
+	// Reset backoff but preserve NeedsManualSync
+	needsManual := state.NeedsManualSync
+	reason := state.FailureReason
+
+	state = SyncState{
+		NeedsManualSync: needsManual,
+		FailureReason:   reason,
+	}
+
+	_ = SaveSyncState(beadsDir, state)
+}