### 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)

}
	}
	if (unsupported_arch) {
		r_error = err;
		return false;
	}
#endif
	
	if (!gradle_build_enabled) {
		String template_err;
		bool dvalid = false;
		bool rvalid = false;
		bool has_export_templates = false;
		if (p_preset->get("custom_template/debug") != "") {
			dvalid = FileAccess::exists(p_preset->get("custom_template/debug"));
			if (!dvalid) {
				template_err += TTR("Custom debug template not found.") + "\n";
			}
		} else {
			has_export_templates |= exists_export_template("android_debug.apk", &template_err);
		}
		if (p_preset->get("custom_template/release") != "") {
			rvalid = FileAccess::exists(p_preset->get("custom_template/release"));
			if (!rvalid) {
				template_err += TTR("Custom release template not found.") + "\n";
			}
		} else {
			has_export_templates |= exists_export_template("android_release.apk", &template_err);
		}
		r_missing_templates = !has_export_templates;