### 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)

encode_uint16(8, &p_manifest.write[ofs + 48]); 
						p_manifest.write[ofs + 50] = 0; 
						p_manifest.write[ofs + 51] = 0x03; 
						encode_uint32(perm_string, &p_manifest.write[ofs + 52]); 
						ofs += 56;
						
						encode_uint16(0x103, &p_manifest.write[ofs]); 
						encode_uint16(16, &p_manifest.write[ofs + 2]); 
						encode_uint32(24, &p_manifest.write[ofs + 4]); 
						encode_uint32(0, &p_manifest.write[ofs + 8]); 
						encode_uint32(-1, &p_manifest.write[ofs + 12]); 
						encode_uint32(-1, &p_manifest.write[ofs + 16]); 
						encode_uint32(attr_uses_permission_string, &p_manifest.write[ofs + 20]); 
						ofs += 24;
					}
					
					memcpy(&p_manifest.write[ofs], manifest_end.ptr(), manifest_end.size());
				}
			} break;
		}
		ofs += size;
	}
	
	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] = p_manifest[i];
	}
	ofs = 0;
	for (int i = 0; i < string_table.size(); i++) {