### 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)

static const String export_method_string[] = {
		"app-store",
		"development",
		"ad-hoc",
		"enterprise"
	};
	static const String storyboard_image_scale_mode[] = {
		"center",
		"scaleAspectFit",
		"scaleAspectFill",
		"scaleToFill"
	};
	String dbg_sign_id = p_preset->get("application/code_sign_identity_debug").operator String().is_empty() ? "iPhone Developer" : p_preset->get("application/code_sign_identity_debug");
	String rel_sign_id = p_preset->get("application/code_sign_identity_release").operator String().is_empty() ? "iPhone Distribution" : p_preset->get("application/code_sign_identity_release");
	bool dbg_manual = !p_preset->get_or_env("application/provisioning_profile_uuid_debug", ENV_IOS_PROFILE_UUID_DEBUG).operator String().is_empty() || (dbg_sign_id != "iPhone Developer");
	bool rel_manual = !p_preset->get_or_env("application/provisioning_profile_uuid_release", ENV_IOS_PROFILE_UUID_RELEASE).operator String().is_empty() || (rel_sign_id != "iPhone Distribution");
	String str;
	String strnew;
	str.parse_utf8((const char *)pfile.ptr(), pfile.size());
	Vector<String> lines = str.split("\n");
	for (int i = 0; i < lines.size(); i++) {
		if (lines[i].find("$binary") != -1) {
			strnew += lines[i].replace("$binary", p_config.binary_name) + "\n";
		} else if (lines[i].find("$modules_buildfile") != -1) {