### 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)

bool gradle_build_enabled = p_preset->get("gradle_build/use_gradle_build");
			int xr_mode_index = p_preset->get("xr_features/xr_mode");
			if (xr_mode_index == XR_MODE_OPENXR && !gradle_build_enabled) {
				return TTR("OpenXR requires \"Use Gradle Build\" to be enabled");
			}
		} else if (p_name == "gradle_build/export_format") {
			bool gradle_build_enabled = p_preset->get("gradle_build/use_gradle_build");
			if (int(p_preset->get("gradle_build/export_format")) == EXPORT_FORMAT_AAB && !gradle_build_enabled) {
				return TTR("\"Export AAB\" is only valid when \"Use Gradle Build\" is enabled.");
			}
		} else if (p_name == "gradle_build/min_sdk") {
			String min_sdk_str = p_preset->get("gradle_build/min_sdk");
			int min_sdk_int = VULKAN_MIN_SDK_VERSION;
			bool gradle_build_enabled = p_preset->get("gradle_build/use_gradle_build");
			if (!min_sdk_str.is_empty()) { 
				if (!gradle_build_enabled) {
					return TTR("\"Min SDK\" can only be overridden when \"Use Gradle Build\" is enabled.");
				}
				if (!min_sdk_str.is_valid_int()) {
					return vformat(TTR("\"Min SDK\" should be a valid integer, but got \"%s\" which is invalid."), min_sdk_str);
				} else {
					min_sdk_int = min_sdk_str.to_int();
					if (min_sdk_int < OPENGL_MIN_SDK_VERSION) {
						return vformat(TTR("\"Min SDK\" cannot be lower than %d, which is the version needed by the Godot library."), OPENGL_MIN_SDK_VERSION);
					}
				}
			}
		} else if (p_name == "gradle_build/target_sdk") {
			String target_sdk_str = p_preset->get("gradle_build/target_sdk");
			int target_sdk_int = DEFAULT_TARGET_SDK_VERSION;