Fix backup status indicator not showing for guests

The backup status indicator feature was incomplete - it added the UI
component but never populated VM/Container LastBackup from actual
backup data. Now SyncGuestBackupTimes() is called after storage
backups and PBS backups are polled, matching each guest's VMID to
its most recent backup timestamp.

Fixes #786

internal/models/models.go

@@ -2,6 +2,7 @@ package models
 
 import (
 	"sort"
+	"strconv"
 	"strings"
 	"sync"
 	"time"
@@ -1118,6 +1119,51 @@ func (s *State) UpdateContainers(containers []Container) {
 	s.LastUpdate = time.Now()
 }
 
+// SyncGuestBackupTimes updates LastBackup on VMs and Containers from storage backups and PBS backups.
+// Call this after updating storage backups or PBS backups to ensure guest backup indicators are accurate.
+func (s *State) SyncGuestBackupTimes() {
+	s.mu.Lock()
+	defer s.mu.Unlock()
+
+	// Build a map of VMID -> latest backup time from all backup sources
+	latestBackup := make(map[int]time.Time)
+
+	// Process PVE storage backups
+	for _, backup := range s.PVEBackups.StorageBackups {
+		if backup.VMID <= 0 {
+			continue
+		}
+		if existing, ok := latestBackup[backup.VMID]; !ok || backup.Time.After(existing) {
+			latestBackup[backup.VMID] = backup.Time
+		}
+	}
+
+	// Process PBS backups (VMID is string, BackupTime is the timestamp)
+	for _, backup := range s.PBSBackups {
+		vmid, err := strconv.Atoi(backup.VMID)
+		if err != nil || vmid <= 0 {
+			continue
+		}
+		if existing, ok := latestBackup[vmid]; !ok || backup.BackupTime.After(existing) {
+			latestBackup[vmid] = backup.BackupTime
+		}
+	}
+
+	// Update VMs
+	for i := range s.VMs {
+		if backupTime, ok := latestBackup[s.VMs[i].VMID]; ok {
+			s.VMs[i].LastBackup = backupTime
+		}
+	}
+
+	// Update Containers
+	for i := range s.Containers {
+		if backupTime, ok := latestBackup[s.Containers[i].VMID]; ok {
+			s.Containers[i].LastBackup = backupTime
+		}
+	}
+}
+
 // UpdateContainersForInstance updates containers for a specific instance, merging with existing containers
 func (s *State) UpdateContainersForInstance(instanceName string, containers []Container) {
 	s.mu.Lock()

internal/monitoring/monitor.go

@@ -8363,6 +8363,9 @@ func (m *Monitor) pollStorageBackupsWithNodes(ctx context.Context, instanceName
 	// Update state with storage backups for this instance
 	m.state.UpdateStorageBackupsForInstance(instanceName, allBackups)
 
+	// Sync backup times to VMs/Containers for backup status indicators
+	m.state.SyncGuestBackupTimes()
+
 	if m.alertManager != nil {
 		snapshot := m.state.GetSnapshot()
 		guestsByKey, guestsByVMID := buildGuestLookups(snapshot, m.guestMetadataStore)
@@ -9289,6 +9292,9 @@ func (m *Monitor) pollPBSBackups(ctx context.Context, instanceName string, clien
 	// Update state
 	m.state.UpdatePBSBackups(instanceName, allBackups)
 
+	// Sync backup times to VMs/Containers for backup status indicators
+	m.state.SyncGuestBackupTimes()
+
 	if m.alertManager != nil {
 		snapshot := m.state.GetSnapshot()
 		guestsByKey, guestsByVMID := buildGuestLookups(snapshot, m.guestMetadataStore)