### 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)

EditorExportPlatformPC::get_export_options(r_options);
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "binary_format/architecture", PROPERTY_HINT_ENUM, "x86_64,x86_32,arm64"), "x86_64"));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "codesign/enable"), false, true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::INT, "codesign/identity_type", PROPERTY_HINT_ENUM, "Select automatically,Use PKCS12 file (specify *.PFX/*.P12 file),Use certificate store (specify SHA-1 hash)", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_SECRET), 0));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "codesign/identity", PROPERTY_HINT_GLOBAL_FILE, "*.pfx,*.p12", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_SECRET), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "codesign/password", PROPERTY_HINT_PASSWORD, "", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_SECRET), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "codesign/timestamp"), true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "codesign/timestamp_server_url"), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::INT, "codesign/digest_algorithm", PROPERTY_HINT_ENUM, "SHA1,SHA256"), 1));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "codesign/description"), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::PACKED_STRING_ARRAY, "codesign/custom_options"), PackedStringArray()));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "application/modify_resources"), true, true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "application/icon", PROPERTY_HINT_FILE, "*.ico,*.png,*.webp,*.svg"), "", false, true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "application/console_wrapper_icon", PROPERTY_HINT_FILE, "*.ico,*.png,*.webp,*.svg"), ""));