Fix: Vue-Litegraph conversion bug with Reroutes (#6330)

## Summary

The private fields triggered an error in intitializing the
linkLayoutSync. Turns out that wasn't necessary anymore.

> [!NOTE]
> Edit: Doing some more investigation, it looks like the slot sync can
also be removed?

## Changes

- **What**: Converts JS private fields to typescript private, adds some
readonly declarations
- **What**: Removes the useLinkLayoutSync usage in useVueNodeLifecycle
- **What**: Removes the useSlotLayoutSync usage in useVueNodeLifecycle

## Review Focus

Was the sync doing something that wouldn't be caught in normal
usage/testing?

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-6330-Fix-Vue-Litegraph-conversion-bug-with-Reroutes-2996d73d3650819ebb24e4aa2fc51c65)
by [Unito](https://www.unito.io)

knip.config.ts

@@ -14,7 +14,7 @@ const config: KnipConfig = {
     },
     'apps/desktop-ui': {
       entry: ['src/main.ts', 'src/i18n.ts'],
-      project: ['src/**/*.{js,ts,vue}', '*.{js,ts,mts}']
+      project: ['src/**/*.{js,ts,vue}']
     },
     'packages/tailwind-utils': {
       project: ['src/**/*.{js,ts}']