### 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 (str == "godot-project-name") {
				
				str = get_project_name(package_name);
			} else {
				String lang = str.substr(str.rfind("-") + 1, str.length()).replace("-", "_");
				if (appnames.has(lang)) {
					str = appnames[lang];
				} else {
					str = get_project_name(package_name);
				}
			}
		}
		string_table.push_back(str);
	}
	
	Vector<uint8_t> ret;
	ret.resize(string_table_begins + string_table.size() * 4);
	for (uint32_t i = 0; i < string_table_begins; i++) {
		ret.write[i] = r_manifest[i];
	}
	int ofs = 0;
	for (int i = 0; i < string_table.size(); i++) {
		encode_uint32(ofs, &ret.write[string_table_begins + i * 4]);
		ofs += string_table[i].length() * 2 + 2 + 2;
	}
	ret.resize(ret.size() + ofs);
	uint8_t *chars = &ret.write[ret.size() - ofs];
	for (int i = 0; i < string_table.size(); i++) {
		String s = string_table[i];
		encode_uint16(s.length(), chars);