More specific class autocompletion in drag-n-drop nodes into editor

### Godot version

4.7-stable

### VS Code version

1.130

### Godot Tools VS Code extension version

2.7.1

### System information

Windows 11

### Problem statement

When I drag and drop a node with script into the editor, the resulting variable type is the most generic one, ignoring the custom class in the script

### Proposed solution

Would be great to add an "use custom classname in drag and drop nodes" feature (either at the core or as a setting) to insert that classname if available.

Desired result for example above:

Start by locating the Godot Tools VS Code extension's drag-and-drop handling and the logic that determines the inserted variable type. Trace how a node's script and custom class are exposed, then verify that dragging a scripted node inserts its custom classname when available without changing generic-node behavior.

Written by the indexing model from the issue text.