### 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)

"WAKE_LOCK",
	"WRITE_APN_SETTINGS",
	"WRITE_CALENDAR",
	"WRITE_CALL_LOG",
	"WRITE_CONTACTS",
	"WRITE_EXTERNAL_STORAGE",
	"WRITE_GSERVICES",
	"WRITE_HISTORY_BOOKMARKS",
	"WRITE_PROFILE",
	"WRITE_SECURE_SETTINGS",
	"WRITE_SETTINGS",
	"WRITE_SMS",
	"WRITE_SOCIAL_STREAM",
	"WRITE_SYNC_SETTINGS",
	"WRITE_USER_DICTIONARY",
	nullptr
};
static const char *SPLASH_IMAGE_EXPORT_PATH = "res/drawable-nodpi/splash.png";
static const char *LEGACY_BUILD_SPLASH_IMAGE_EXPORT_PATH = "res/drawable-nodpi-v4/splash.png";
static const char *SPLASH_BG_COLOR_PATH = "res/drawable-nodpi/splash_bg_color.png";
static const char *LEGACY_BUILD_SPLASH_BG_COLOR_PATH = "res/drawable-nodpi-v4/splash_bg_color.png";
static const char *SPLASH_CONFIG_PATH = "res://android/build/res/drawable/splash_drawable.xml";
static const char *GDEXTENSION_LIBS_PATH = "res://android/build/libs/gdextensionlibs.json";
static const int icon_densities_count = 6;
static const char *launcher_icon_option = PNAME("launcher_icons/main_192x192");
static const char *launcher_adaptive_icon_foreground_option = PNAME("launcher_icons/adaptive_foreground_432x432");
static const char *launcher_adaptive_icon_background_option = PNAME("launcher_icons/adaptive_background_432x432");
static const LauncherIcon launcher_icons[icon_densities_count] = {
	{ "res/mipmap-xxxhdpi-v4/icon.png", 192 },
	{ "res/mipmap-xxhdpi-v4/icon.png", 144 },