### 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)

export_warning->hide();
		}
		export_error->hide();
		export_templates_error->hide();
		export_button->set_disabled(false);
	}
	custom_features->set_text(current->get_custom_features());
	_update_feature_list();
	_update_export_all();
	child_controls_changed();
	if ((feature_set.has("s3tc") || feature_set.has("bptc")) && !ResourceImporterTextureSettings::should_import_s3tc_bptc()) {
		export_texture_format_error->show_for_texture_format("S3TC/BPTC", "rendering/textures/vram_compression/import_s3tc_bptc");
	} else if ((feature_set.has("etc2") || feature_set.has("astc")) && !ResourceImporterTextureSettings::should_import_etc2_astc()) {
		export_texture_format_error->show_for_texture_format("ETC2/ASTC", "rendering/textures/vram_compression/import_etc2_astc");
	} else {
		export_texture_format_error->hide();
	}
	String enc_in_filters_str = current->get_enc_in_filter();
	String enc_ex_filters_str = current->get_enc_ex_filter();
	if (!updating_enc_filters) {
		enc_in_filters->set_text(enc_in_filters_str);
		enc_ex_filters->set_text(enc_ex_filters_str);
	}
	bool enc_pck_mode = current->get_enc_pck();
	enc_pck->set_pressed(enc_pck_mode);
	enc_directory->set_disabled(!enc_pck_mode);
	enc_in_filters->set_editable(enc_pck_mode);
	enc_ex_filters->set_editable(enc_pck_mode);
	script_key->set_editable(enc_pck_mode);
	bool enc_directory_mode = current->get_enc_directory();