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)

tests-ui/tests/litegraph/core/__snapshots__/LGraph.test.ts.snap

@@ -274,6 +274,7 @@ LGraph {
   "filter": undefined,
   "fixedtime": 0,
   "fixedtime_lapse": 0.01,
+  "floatingLinksInternal": Map {},
   "globaltime": 0,
   "id": "b4e984f1-b421-4d24-b8b4-ff895793af13",
   "iteration": 0,
@@ -284,6 +285,7 @@ LGraph {
   "nodes_executedAction": [],
   "nodes_executing": [],
   "onTrigger": undefined,
+  "reroutesInternal": Map {},
   "revision": 0,
   "runningtime": 0,
   "starttime": 0,