fix: stabilize nested subgraph promoted widget resolution (#9282)

## Summary

Fix multiple issues with promoted widget resolution in nested subgraphs,
ensuring correct value propagation, slot matching, and rendering for
deeply nested promoted widgets.

## Changes

- **What**: Stabilize nested subgraph promoted widget resolution chain
- Use deep source keys for promoted widget values in Vue rendering mode
- Resolve effective widget options from the source widget instead of the
promoted view
  - Stabilize slot resolution for nested promoted widgets
  - Preserve combo value rendering for promoted subgraph widgets
- Prevent subgraph definition deletion while other nodes still reference
the same type
  - Clean up unused exported resolution types

## Review Focus

- `resolveConcretePromotedWidget.ts` — new recursive resolution logic
for deeply nested promoted widgets
- `useGraphNodeManager.ts` — option extraction now uses
`effectiveWidget` for promoted widgets
- `SubgraphNode.ts` — unpack no longer force-deletes definitions
referenced by other nodes

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-9282-fix-stabilize-nested-subgraph-promoted-widget-resolution-3146d73d365081208a4fe931bb7569cf)
by [Unito](https://www.unito.io)

---------

Co-authored-by: Amp <amp@ampcode.com>
Co-authored-by: GitHub Action <action@github.com>

src/lib/litegraph/src/LGraph.test.ts

@@ -634,4 +634,25 @@ describe('Subgraph Unpacking', () => {
     expect(unpackedTarget.inputs[0].link).not.toBeNull()
     expect(unpackedTarget.inputs[1].link).toBeNull()
   })
+
+  it('keeps subgraph definition when unpacking one instance while another remains', () => {
+    const rootGraph = new LGraph()
+    const subgraph = createSubgraphOnGraph(rootGraph)
+
+    const firstInstance = createTestSubgraphNode(subgraph, { pos: [100, 100] })
+    const secondInstance = createTestSubgraphNode(subgraph, { pos: [300, 100] })
+    secondInstance.id = 2
+    rootGraph.add(firstInstance)
+    rootGraph.add(secondInstance)
+
+    rootGraph.unpackSubgraph(firstInstance)
+
+    expect(rootGraph.subgraphs.has(subgraph.id)).toBe(true)
+
+    const serialized = rootGraph.serialize()
+    const definitionIds =
+      serialized.definitions?.subgraphs?.map((definition) => definition.id) ??
+      []
+    expect(definitionIds).toContain(subgraph.id)
+  })
 })