feat: Add remote sync for project clones

Fetch remote changes before agents start working so they build on
up-to-date code. Adds ProjectSyncManager with git fetch + ff-only
merge of defaultBranch, integrated into phase dispatch to sync
before branch creation.

- Schema: lastFetchedAt column on projects table (migration 0029)
- Events: project:synced, project:sync_failed
- Phase dispatch: sync all linked projects before creating branches
- tRPC: syncProject, syncAllProjects, getProjectSyncStatus
- CLI: cw project sync [name] --all, cw project status [name]
- Frontend: sync button + ahead/behind badge on projects settings

apps/web/src/routes/settings/projects.tsx

@@ -1,6 +1,6 @@
 import { useState } from 'react'
 import { createFileRoute } from '@tanstack/react-router'
-import { Pencil, Plus, Trash2 } from 'lucide-react'
+import { Pencil, Plus, RefreshCw, Trash2 } from 'lucide-react'
 import { trpc } from '@/lib/trpc'
 import { Card, CardContent } from '@/components/ui/card'
 import { Button } from '@/components/ui/button'
@@ -92,11 +92,24 @@ function ProjectsSettingsPage() {
   )
 }
 
+function formatRelativeTime(date: Date | string | null): string {
+  if (!date) return 'never synced'
+  const d = typeof date === 'string' ? new Date(date) : date
+  const seconds = Math.floor((Date.now() - d.getTime()) / 1000)
+  if (seconds < 60) return 'just now'
+  const minutes = Math.floor(seconds / 60)
+  if (minutes < 60) return `${minutes}m ago`
+  const hours = Math.floor(minutes / 60)
+  if (hours < 24) return `${hours}h ago`
+  const days = Math.floor(hours / 24)
+  return `${days}d ago`
+}
+
 function ProjectCard({
   project,
   onDelete,
 }: {
-  project: { id: string; name: string; url: string; defaultBranch: string }
+  project: { id: string; name: string; url: string; defaultBranch: string; lastFetchedAt: Date | null }
   onDelete: () => void
 }) {
   const [editing, setEditing] = useState(false)
@@ -115,6 +128,26 @@ function ProjectCard({
     },
   })
 
+  const syncMutation = trpc.syncProject.useMutation({
+    onSuccess: (result) => {
+      void utils.listProjects.invalidate()
+      void utils.getProjectSyncStatus.invalidate({ id: project.id })
+      if (result.success) {
+        toast.success(`Synced ${result.projectName}`)
+      } else {
+        toast.error(`Sync failed: ${result.error}`)
+      }
+    },
+    onError: (err) => {
+      toast.error(`Sync failed: ${err.message}`)
+    },
+  })
+
+  const syncStatusQuery = trpc.getProjectSyncStatus.useQuery(
+    { id: project.id },
+    { refetchInterval: 60_000 },
+  )
+
   function saveEdit() {
     const trimmed = editValue.trim()
     if (!trimmed || trimmed === project.defaultBranch) {
@@ -125,6 +158,8 @@ function ProjectCard({
     updateMutation.mutate({ id: project.id, defaultBranch: trimmed })
   }
 
+  const syncStatus = syncStatusQuery.data
+
   return (
     <Card>
       <CardContent className="flex items-center gap-4 py-4">
@@ -164,7 +199,27 @@ function ProjectCard({
               </button>
             )}
           </div>
+          <div className="flex items-center gap-3 text-xs text-muted-foreground">
+            <span>Synced: {formatRelativeTime(project.lastFetchedAt)}</span>
+            {syncStatus && (syncStatus.ahead > 0 || syncStatus.behind > 0) && (
+              <span className="font-mono">
+                {syncStatus.ahead > 0 && <span className="text-status-success-fg">+{syncStatus.ahead}</span>}
+                {syncStatus.ahead > 0 && syncStatus.behind > 0 && ' / '}
+                {syncStatus.behind > 0 && <span className="text-status-warning-fg">-{syncStatus.behind}</span>}
+              </span>
+            )}
+          </div>
         </div>
+        <Button
+          variant="ghost"
+          size="icon"
+          className="shrink-0 text-muted-foreground"
+          onClick={() => syncMutation.mutate({ id: project.id })}
+          disabled={syncMutation.isPending}
+          title="Sync from remote"
+        >
+          <RefreshCw className={`h-4 w-4 ${syncMutation.isPending ? 'animate-spin' : ''}`} />
+        </Button>
         <Button
           variant="ghost"
           size="icon"