[refactor] Extract manager composables and execution utils (#9163)

## Summary
Extracts inline logic from manager components into dedicated composables
and utilities, and adds a cyclic subgraph fix.

## Changes
- **`usePackInstall`**: New composable extracted from
`PackInstallButton.vue` — handles conflict detection, payload
construction, and `Promise.allSettled`-based batch installation
- **`useApplyChanges`**: New shared composable extracted from
`ManagerProgressToast.vue` — manages ComfyUI restart flow with reconnect
timeout and post-reconnect refresh
- **`executionIdUtil`**: New utility (`getAncestorExecutionIds`,
`getParentExecutionIds`, `buildSubgraphExecutionPaths`) with unit tests;
fixes infinite recursion on cyclic subgraph definitions

## Review Focus
- `useApplyChanges` reconnect timeout (2 min) and setting restore logic
- `buildSubgraphExecutionPaths` visited-set guard for cyclic subgraph
defs

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-9163-refactor-Extract-manager-composables-and-execution-utils-3116d73d365081f293d3d5484775ad48)
by [Unito](https://www.unito.io)

src/utils/executionIdUtil.test.ts

@@ -0,0 +1,98 @@
+import { describe, expect, it } from 'vitest'
+
+import type { ComfyNode } from '@/platform/workflow/validation/schemas/workflowSchema'
+import {
+  buildSubgraphExecutionPaths,
+  getAncestorExecutionIds,
+  getParentExecutionIds
+} from '@/utils/executionIdUtil'
+
+function node(id: number, type: string): ComfyNode {
+  return { id, type } as ComfyNode
+}
+
+function subgraphDef(id: string, nodes: ComfyNode[]) {
+  return { id, name: id, nodes, inputNode: {}, outputNode: {} }
+}
+
+describe('getAncestorExecutionIds', () => {
+  it('returns only itself for a root node', () => {
+    expect(getAncestorExecutionIds('65')).toEqual(['65'])
+  })
+
+  it('returns all ancestors including self for nested IDs', () => {
+    expect(getAncestorExecutionIds('65:70')).toEqual(['65', '65:70'])
+    expect(getAncestorExecutionIds('65:70:63')).toEqual([
+      '65',
+      '65:70',
+      '65:70:63'
+    ])
+  })
+})
+
+describe('getParentExecutionIds', () => {
+  it('returns empty for a root node', () => {
+    expect(getParentExecutionIds('65')).toEqual([])
+  })
+
+  it('returns all ancestors excluding self for nested IDs', () => {
+    expect(getParentExecutionIds('65:70')).toEqual(['65'])
+    expect(getParentExecutionIds('65:70:63')).toEqual(['65', '65:70'])
+  })
+})
+
+describe('buildSubgraphExecutionPaths', () => {
+  it('returns empty map when there are no subgraph definitions', () => {
+    expect(buildSubgraphExecutionPaths([node(5, 'SomeNode')], [])).toEqual(
+      new Map()
+    )
+  })
+
+  it('returns empty map when no root node matches a subgraph type', () => {
+    const def = subgraphDef('def-A', [])
+    expect(
+      buildSubgraphExecutionPaths([node(5, 'UnrelatedNode')], [def])
+    ).toEqual(new Map())
+  })
+
+  it('maps a single subgraph instance to its execution path', () => {
+    const def = subgraphDef('def-A', [])
+    const result = buildSubgraphExecutionPaths([node(5, 'def-A')], [def])
+    expect(result.get('def-A')).toEqual(['5'])
+  })
+
+  it('collects multiple instances of the same subgraph type', () => {
+    const def = subgraphDef('def-A', [])
+    const result = buildSubgraphExecutionPaths(
+      [node(5, 'def-A'), node(10, 'def-A')],
+      [def]
+    )
+    expect(result.get('def-A')).toEqual(['5', '10'])
+  })
+
+  it('builds nested execution paths for subgraphs within subgraphs', () => {
+    const innerDef = subgraphDef('def-B', [])
+    const outerDef = subgraphDef('def-A', [node(70, 'def-B')])
+    const result = buildSubgraphExecutionPaths(
+      [node(5, 'def-A')],
+      [outerDef, innerDef]
+    )
+    expect(result.get('def-A')).toEqual(['5'])
+    expect(result.get('def-B')).toEqual(['5:70'])
+  })
+
+  it('does not recurse infinitely on self-referential subgraph definitions', () => {
+    const cyclicDef = subgraphDef('def-A', [node(70, 'def-A')])
+    expect(() =>
+      buildSubgraphExecutionPaths([node(5, 'def-A')], [cyclicDef])
+    ).not.toThrow()
+  })
+
+  it('does not recurse infinitely on mutually cyclic subgraph definitions', () => {
+    const defA = subgraphDef('def-A', [node(70, 'def-B')])
+    const defB = subgraphDef('def-B', [node(80, 'def-A')])
+    expect(() =>
+      buildSubgraphExecutionPaths([node(5, 'def-A')], [defA, defB])
+    ).not.toThrow()
+  })
+})

src/utils/executionIdUtil.ts

@@ -0,0 +1,71 @@
+import type { NodeExecutionId } from '@/types/nodeIdentification'
+import type { ComfyNode } from '@/platform/workflow/validation/schemas/workflowSchema'
+import { isSubgraphDefinition } from '@/platform/workflow/validation/schemas/workflowSchema'
+
+/**
+ * Returns all ancestor execution IDs for a given execution ID, including itself.
+ *
+ * Example: "65:70:63" → ["65", "65:70", "65:70:63"]
+ * @knipIgnoreUsedByStackedPR
+ */
+export function getAncestorExecutionIds(
+  executionId: string | NodeExecutionId
+): NodeExecutionId[] {
+  const parts = executionId.split(':')
+  return Array.from({ length: parts.length }, (_, i) =>
+    parts.slice(0, i + 1).join(':')
+  )
+}
+
+/**
+ * Returns all ancestor execution IDs for a given execution ID, excluding itself.
+ *
+ * Example: "65:70:63" → ["65", "65:70"]
+ * @knipIgnoreUsedByStackedPR
+ */
+export function getParentExecutionIds(
+  executionId: string | NodeExecutionId
+): NodeExecutionId[] {
+  return getAncestorExecutionIds(executionId).slice(0, -1)
+}
+
+/**
+ * "def-A" → ["5", "10"] for each container node instantiating that subgraph definition.
+ * @knipIgnoreUsedByStackedPR
+ */
+export function buildSubgraphExecutionPaths(
+  rootNodes: ComfyNode[],
+  allSubgraphDefs: unknown[]
+): Map<string, string[]> {
+  const subgraphDefMap = new Map(
+    allSubgraphDefs.filter(isSubgraphDefinition).map((s) => [s.id, s])
+  )
+  const pathMap = new Map<string, string[]>()
+  const visited = new Set<string>()
+
+  const build = (nodes: ComfyNode[], parentPrefix: string) => {
+    for (const n of nodes ?? []) {
+      if (typeof n.type !== 'string' || !subgraphDefMap.has(n.type)) continue
+      const path = parentPrefix ? `${parentPrefix}:${n.id}` : String(n.id)
+      const existing = pathMap.get(n.type)
+      if (existing) {
+        existing.push(path)
+      } else {
+        pathMap.set(n.type, [path])
+      }
+
+      if (visited.has(n.type)) continue
+      visited.add(n.type)
+
+      const innerDef = subgraphDefMap.get(n.type)
+      if (innerDef) {
+        build(innerDef.nodes, path)
+      }
+
+      visited.delete(n.type)
+    }
+  }
+
+  build(rootNodes, '')
+  return pathMap
+}