### Godot version

Godot 4.1 Release Candidate 1

### System information

Godot v4.1.rc1.mono - Windows 10.0.19045 - Vulkan (Forward+) - dedicated NVIDIA GeForce RTX 3080 (NVIDIA; 31.0.15.1694) - AMD Ryzen 7 3800X 8-Core Processor (16 Threads)

### Issue description

Godot 4.1 RC1 does not update the [Export]ed members or the name of a type/class in inspector when
- ... creating a new class.cs file that inherits from node/resource
- ... renaming a class from A.cs to B.cs
- ... removing and adding the class to a Node/Resource
- ... adding enum values to an existing enum (doesnt matter if its [Flags])
- ... adding/removing [Export] on any member variable
- ... (and probably more use cases)
![image](https://github.com/godotengine/godot/assets/45302427/d11a515e-47b6-40a8-af81-670407bfda1a)

It only works when Project > "Reload Current Project"
![image](https://github.com/godotengine/godot/assets/45302427/8de25a6f-d851-4d58-881b-673060d89741)


### Steps to reproduce

Create a new .cs file that inherits from a Node or Resource 
Assign it a Node/Resource
Add any sort of variables to the .cs file
Add the [Export] attribute to these variables/members
Build the Code using Alt+B
Watch what happens in the inspector: Nothing!
If nothing happens: Project > Reload Current Project

Test Project attached below

### Minimal reproduction project

[inspector-update-fails.zip](https://github.com/godotengine/godot/files/11886640/inspector-update-fails.zip)

#include "editor/editor_node.h"
#include "editor/editor_settings.h"
#include "editor/inspector_dock.h"
#include "editor/node_dock.h"
#endif
#include <stdint.h>
#define CACHED_STRING_NAME(m_var) (CSharpLanguage::get_singleton()->get_string_names().m_var)
const Vector<String> ignored_types = { "PhysicsServer2DExtension", "PhysicsServer3DExtension" };
#ifdef TOOLS_ENABLED
static bool _create_project_solution_if_needed() {
	CRASH_COND(CSharpLanguage::get_singleton()->get_godotsharp_editor() == nullptr);
	return CSharpLanguage::get_singleton()->get_godotsharp_editor()->call("CreateProjectSolutionIfNeeded");
}
#endif
CSharpLanguage *CSharpLanguage::singleton = nullptr;
GDExtensionInstanceBindingCallbacks CSharpLanguage::_instance_binding_callbacks = {
	&_instance_binding_create_callback,
	&_instance_binding_free_callback,
	&_instance_binding_reference_callback
};
String CSharpLanguage::get_name() const {
	return "C#";
}
String CSharpLanguage::get_type() const {
	return "CSharpScript";
}
String CSharpLanguage::get_extension() const {
	return "cs";
}
void CSharpLanguage::init() {