Cleanup: Litegraph/Vue synchronization work (#5789)

## Summary

Cleanup and fixes to the existing syncing logic.

## Review Focus

This is probably enough to review and test now.

Main things that should still work: 
- moving nodes around
- adding new ones
- switching back and forth between Vue and Litegraph

Let me know if you find any bugs that weren't already present there.

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-5789-WIP-Litegraph-Vue-synchronization-work-27a6d73d3650811682cacacb82367b9e)
by [Unito](https://www.unito.io)

browser_tests/tests/vueNodes/interactions/links/linkInteraction.spec.ts

@@ -100,7 +100,7 @@ test.describe('Vue Node Link Interaction', () => {
 
     const linkDetails = await comfyPage.page.evaluate((sourceId) => {
       const app = window['app']
-      const graph = app?.canvas?.graph ?? app?.graph
+      const graph = app?.canvas?.graph
       if (!graph) return null
 
       const source = graph.getNodeById(sourceId)
@@ -164,7 +164,7 @@ test.describe('Vue Node Link Interaction', () => {
 
     const graphLinkCount = await comfyPage.page.evaluate((sourceId) => {
       const app = window['app']
-      const graph = app?.canvas?.graph ?? app?.graph
+      const graph = app?.canvas?.graph
       if (!graph) return 0
 
       const source = graph.getNodeById(sourceId)
@@ -207,7 +207,7 @@ test.describe('Vue Node Link Interaction', () => {
 
     const graphLinkCount = await comfyPage.page.evaluate((sourceId) => {
       const app = window['app']
-      const graph = app?.canvas?.graph ?? app?.graph
+      const graph = app?.canvas?.graph
       if (!graph) return 0
 
       const source = graph.getNodeById(sourceId)