### Tested versions

Godot Engine v4.2.stable.official.46dc27791

### System information

Windows 10

### Issue description

When exporting to web, Godot fails with this error in the console:

> scene/main/window.cpp:884 - Attempting to make child window exclusive, but the parent window already has another exclusive child. This window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->VBoxContainer@<!-- -->137/@<!-- -->AcceptDialog@<!-- -->411, parent window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559, current exclusive child window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->ProgressDialog@<!-- -->17444

![a](https://github.com/godotengine/godot/assets/2000051/bf9d22aa-d3fe-4e11-bff6-c387e740fe90)

This happens for newly created empty projects.


### Steps to reproduce

1. Open the attached project (or create a new project).
2. Project->Export->Export All
3. Observe the console error.  No output files are generated.


### Minimal reproduction project (MRP)

[export_test.zip](https://github.com/godotengine/godot/files/13574810/export_test.zip)

#include "editor_export_platform.h"
#include "core/config/project_settings.h"
#include "core/crypto/crypto_core.h"
#include "core/extension/gdextension.h"
#include "core/io/file_access_encrypted.h"
#include "core/io/file_access_pack.h" 
#include "core/io/zip_io.h"
#include "core/version.h"
#include "editor/editor_file_system.h"
#include "editor/editor_node.h"
#include "editor/editor_paths.h"
#include "editor/editor_scale.h"
#include "editor/editor_settings.h"
#include "editor/editor_string_names.h"
#include "editor/export/editor_export.h"
#include "editor/plugins/script_editor_plugin.h"
#include "editor_export_plugin.h"
#include "scene/resources/image_texture.h"
#include "scene/resources/packed_scene.h"
static int _get_pad(int p_alignment, int p_n) {
	int rest = p_n % p_alignment;
	int pad = 0;
	if (rest > 0) {
		pad = p_alignment - rest;
	};
	return pad;
}
#define PCK_PADDING 16
bool EditorExportPlatform::fill_log_messages(RichTextLabel *p_log, Error p_err) {