### 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 (p_preset->get("codesign/timestamp_server") != "") {
#ifdef WINDOWS_ENABLED
			args.push_back("/tr");
			args.push_back(p_preset->get("codesign/timestamp_server_url"));
			args.push_back("/td");
			if ((int)p_preset->get("codesign/digest_algorithm") == 0) {
				args.push_back("sha1");
			} else {
				args.push_back("sha256");
			}
#else
			args.push_back("-ts");
			args.push_back(p_preset->get("codesign/timestamp_server_url"));
#endif
		} else {
			add_message(EXPORT_MESSAGE_WARNING, TTR("Code Signing"), TTR("Invalid timestamp server."));
			return FAILED;
		}
	}
	
#ifdef WINDOWS_ENABLED
	args.push_back("/fd");
#else
	args.push_back("-h");
#endif
	if ((int)p_preset->get("codesign/digest_algorithm") == 0) {
		args.push_back("sha1");
	} else {
		args.push_back("sha256");
	}