### 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 (four_bits < 10) {
			return ('0' + four_bits);
		}
		return 'A' + (four_bits - 10);
	}
	static String _hex_pad(uint32_t num) {
		Vector<char> ret;
		ret.resize(sizeof(num) * 2);
		for (uint64_t i = 0; i < sizeof(num) * 2; ++i) {
			uint8_t four_bits = (num >> (sizeof(num) * 8 - (i + 1) * 4)) & 0xF;
			ret.write[i] = _hex_char(four_bits);
		}
		return String::utf8(ret.ptr(), ret.size());
	}
public:
	uint32_t high_bits;
	uint32_t mid_bits;
	uint32_t low_bits;
	String str() const {
		return _hex_pad(high_bits) + _hex_pad(mid_bits) + _hex_pad(low_bits);
	}
	PbxId &operator++() {