fix(liveview): nest docker children, apply theme & custom style

- Live view rebuilt parent map from proxmox/group only, so docker_container
  (and any vm/lxc with container_mode=true) lost parentId and rendered
  outside its host. Match App.tsx logic: include any node with
  container_mode=true.
- Live view ignored viewport.theme_id and custom_style on load, so the
  shared canvas always rendered in default theme. Apply both like the
  authenticated canvas does.
- Backend /liveview response now includes custom_style from CanvasState.

Adds regression tests on both ends.

frontend/src/components/LiveView.tsx

@@ -29,7 +29,7 @@ import { nodeTypes } from '@/components/canvas/nodes/nodeTypes'
 import { edgeTypes } from '@/components/canvas/edges/edgeTypes'
 import { deserializeApiNode, deserializeApiEdge, type ApiNode, type ApiEdge } from '@/utils/canvasSerializer'
 import { liveviewApi } from '@/api/client'
-import type { NodeData } from '@/types'
+import type { NodeData, CustomStyleDef } from '@/types'
 
 const STANDALONE = import.meta.env.VITE_STANDALONE === 'true'
 const STORAGE_KEY = 'homelable_canvas'
@@ -40,6 +40,8 @@ function LiveViewCanvas() {
   const { nodes, edges, loadCanvas, fitViewPending, clearFitViewPending } = useCanvasStore()
   const { fitView } = useReactFlow()
   const activeTheme = useThemeStore((s) => s.activeTheme)
+  const setTheme = useThemeStore((s) => s.setTheme)
+  const setCustomStyle = useThemeStore((s) => s.setCustomStyle)
   const theme = THEMES[activeTheme]
   // Derive initial view state synchronously (avoids calling setState inside an effect):
   // - standalone → always ready (localStorage, no key required)
@@ -73,9 +75,12 @@ function LiveViewCanvas() {
         const { nodes: apiNodes, edges: apiEdges } = res.data
         const proxmoxMap = new Map<string, boolean>(
           (apiNodes as ApiNode[])
-            .filter((n: ApiNode) => n.type === 'proxmox' || n.type === 'group')
-            .map((n: ApiNode) => [n.id, n.type === 'group' ? true : n.container_mode !== false])
+            .filter((n: ApiNode) => n.type === 'group' || n.container_mode === true)
+            .map((n: ApiNode) => [n.id, true])
         )
+        const savedTheme = res.data.viewport?.theme_id
+        if (savedTheme) setTheme(savedTheme)
+        if (res.data.custom_style) setCustomStyle(res.data.custom_style as CustomStyleDef)
         loadCanvas(
           (apiNodes as ApiNode[]).map((n) => deserializeApiNode(n, proxmoxMap)),
           (apiEdges as ApiEdge[]).map(deserializeApiEdge),

frontend/src/components/__tests__/LiveView.test.tsx

@@ -1,6 +1,7 @@
 import { describe, it, expect, vi, beforeEach } from 'vitest'
 import { render, screen, waitFor } from '@testing-library/react'
 import { useCanvasStore } from '@/stores/canvasStore'
+import { useThemeStore } from '@/stores/themeStore'
 
 // ── Mock heavy dependencies ────────────────────────────────────────────────
 
@@ -124,6 +125,55 @@ describe('LiveView (non-standalone)', () => {
     expect(nodes.find((n) => n.id === 'n1')).toBeDefined()
   })
 
+  // ── Nested children (docker_container inside docker_host) ────────────────
+
+  it('nests docker_container under docker_host parent (container_mode=true)', async () => {
+    setSearch('?key=valid')
+    const nestedPayload = {
+      data: {
+        nodes: [
+          {
+            id: 'host', type: 'docker', label: 'Docker Host', status: 'online',
+            services: [], pos_x: 0, pos_y: 0, container_mode: true,
+            created_at: '2024-01-01T00:00:00Z', updated_at: '2024-01-01T00:00:00Z',
+          },
+          {
+            id: 'ctr', type: 'docker_container', label: 'nginx', status: 'online',
+            services: [], pos_x: 20, pos_y: 30, parent_id: 'host',
+            created_at: '2024-01-01T00:00:00Z', updated_at: '2024-01-01T00:00:00Z',
+          },
+        ],
+        edges: [],
+        viewport: { x: 0, y: 0, zoom: 1 },
+      },
+    }
+    vi.mocked(liveviewApi.load).mockResolvedValue(nestedPayload as never)
+    render(<LiveView />)
+    await waitFor(() => expect(screen.getByTestId('react-flow')).toBeDefined())
+    const ctr = useCanvasStore.getState().nodes.find((n) => n.id === 'ctr')
+    expect(ctr?.parentId).toBe('host')
+    expect(ctr?.extent).toBe('parent')
+  })
+
+  // ── Theme + custom_style applied from payload ────────────────────────────
+
+  it('applies viewport.theme_id and custom_style from the payload', async () => {
+    setSearch('?key=valid')
+    const styledPayload = {
+      data: {
+        nodes: [],
+        edges: [],
+        viewport: { x: 0, y: 0, zoom: 1, theme_id: 'matrix' },
+        custom_style: { fontFamily: 'Inter', nodeRadius: 12 },
+      },
+    }
+    vi.mocked(liveviewApi.load).mockResolvedValue(styledPayload as never)
+    render(<LiveView />)
+    await waitFor(() => expect(screen.getByTestId('react-flow')).toBeDefined())
+    expect(useThemeStore.getState().activeTheme).toBe('matrix')
+    expect(useThemeStore.getState().customStyle).toEqual({ fontFamily: 'Inter', nodeRadius: 12 })
+  })
+
   // ── No editing props passed ───────────────────────────────────────────────
 
   it('does not show any Access Denied when key is valid', async () => {