### 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)

const int UTF8_FLAG = 0x00000100;
	uint32_t string_block_len = decode_uint32(&r_manifest[16]);
	uint32_t string_count = decode_uint32(&r_manifest[20]);
	uint32_t string_flags = decode_uint32(&r_manifest[28]);
	const uint32_t string_table_begins = 40;
	Vector<String> string_table;
	String package_name = p_preset->get("package/name");
	Dictionary appnames = GLOBAL_GET("application/config/name_localized");
	for (uint32_t i = 0; i < string_count; i++) {
		uint32_t offset = decode_uint32(&r_manifest[string_table_begins + i * 4]);
		offset += string_table_begins + string_count * 4;
		String str = _parse_string(&r_manifest[offset], string_flags & UTF8_FLAG);
		if (str.begins_with("godot-project-name")) {