### 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_uint32(version_value, &p_manifest.write[ofs + 16]); 
								ofs += 20;
							}
							
							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_feature_string, &p_manifest.write[ofs + 20]); 
							ofs += 24;
						}
						memcpy(&p_manifest.write[ofs], manifest_end.ptr(), manifest_end.size());
						ofs -= 24; 
					}
				}
				if (tname == "manifest") {
					
					Vector<uint8_t> manifest_end;
					uint32_t manifest_cur_size = p_manifest.size();
					manifest_end.resize(p_manifest.size() - ofs);
					memcpy(manifest_end.ptrw(), &p_manifest[ofs], manifest_end.size());
					int32_t attr_name_string = string_table.find("name");
					ERR_FAIL_COND_MSG(attr_name_string == -1, "Template does not have 'name' attribute.");
					int32_t ns_android_string = string_table.find("android");
					ERR_FAIL_COND_MSG(ns_android_string == -1, "Template does not have 'android' namespace.");
					int32_t attr_uses_permission_string = string_table.find("uses-permission");
					if (attr_uses_permission_string == -1) {
						string_table.push_back("uses-permission");