### 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)

int iofs = ofs + 8;
				uint32_t name = decode_uint32(&p_manifest[iofs + 12]);
				String tname = string_table[name];
				if (tname == "uses-feature") {
					Vector<String> feature_names;
					Vector<bool> feature_required_list;
					Vector<int> feature_versions;
					if (_uses_vulkan()) {
						
						feature_names.push_back("android.hardware.vulkan.level");
						feature_required_list.push_back(false);
						feature_versions.push_back(1);
						
						feature_names.push_back("android.hardware.vulkan.version");
						feature_required_list.push_back(true);
						feature_versions.push_back(0x400003); 
					}
					if (feature_names.size() > 0) {
						ofs += 24; 
						
						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("http://schemas.android.com/apk/res/android");
						if (ns_android_string == -1) {
							string_table.push_back("http://schemas.android.com/apk/res/android");
							ns_android_string = string_table.size() - 1;