Support "control after generate" in vue (#6985)

Continuation of #6034 with
- Updated synchronization for seed
- Properly truncates the displayed widget value for the button
- Synchronizes control after generate state with litegraph and allows
for serialization

Several issues from original PR have not (yet) been addressed, but are
likely better moved to future PR
- fix step value being 10 (legacy system)
- ensure it works with COMBO (Fixed in #7095)
- ensure it works with FLOAT (Fixed in #7095)
- either implement or remove the config button functionality - think it
should open settings?

<img width="280" height="694" alt="image"
src="https://github.com/user-attachments/assets/f36f1cb0-237d-4bfc-bff1-e4976775cf98"
/>

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-6985-Support-control-after-generate-in-vue-2b86d73d365081d8b01ce489d887ff00)
by [Unito](https://www.unito.io)

---------

Co-authored-by: bymyself <cbyrne@comfy.org>
Co-authored-by: github-actions <github-actions@github.com>

src/composables/graph/useGraphNodeManager.ts

@@ -20,7 +20,8 @@ import type { NodeId } from '@/renderer/core/layout/types'
 import type { InputSpec } from '@/schemas/nodeDef/nodeDefSchemaV2'
 import { isDOMWidget } from '@/scripts/domWidget'
 import { useNodeDefStore } from '@/stores/nodeDefStore'
-import type { WidgetValue } from '@/types/simplifiedWidget'
+import type { WidgetValue, SafeControlWidget } from '@/types/simplifiedWidget'
+import { normalizeControlOption } from '@/types/simplifiedWidget'
 
 import type {
   LGraph,
@@ -47,6 +48,7 @@ export interface SafeWidgetData {
   spec?: InputSpec
   slotMetadata?: WidgetSlotMetadata
   isDOMWidget?: boolean
+  controlWidget?: SafeControlWidget
   borderStyle?: string
 }
 
@@ -84,6 +86,17 @@ export interface GraphNodeManager {
   cleanup(): void
 }
 
+function getControlWidget(widget: IBaseWidget): SafeControlWidget | undefined {
+  const cagWidget = widget.linkedWidgets?.find(
+    (w) => w.name == 'control_after_generate'
+  )
+  if (!cagWidget) return
+  return {
+    value: normalizeControlOption(cagWidget.value),
+    update: (value) => (cagWidget.value = normalizeControlOption(value))
+  }
+}
+
 export function safeWidgetMapper(
   node: LGraphNode,
   slotMetadata: Map<string, WidgetSlotMetadata>
@@ -122,7 +135,8 @@ export function safeWidgetMapper(
         label: widget.label,
         options: widget.options,
         spec,
-        slotMetadata: slotInfo
+        slotMetadata: slotInfo,
+        controlWidget: getControlWidget(widget)
       }
     } catch (error) {
       return {