### 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 "export_plugin.h"
#include "logo_svg.gen.h"
#include "run_icon_svg.gen.h"
#include "core/config/project_settings.h"
#include "core/io/image_loader.h"
#include "editor/editor_node.h"
#include "editor/editor_paths.h"
#include "editor/editor_scale.h"
#include "editor/editor_string_names.h"
#include "editor/export/editor_export.h"
#include "modules/modules_enabled.gen.h" 
#ifdef MODULE_SVG_ENABLED
#include "modules/svg/image_loader_svg.h"
#endif
Error EditorExportPlatformWindows::_process_icon(const Ref<EditorExportPreset> &p_preset, const String &p_src_path, const String &p_dst_path) {