Editor freezes when creating a new project after moving Godot to the second screen

### Tested versions

4.2.1 stable official

### System information

Windows 10, NVidia GeForce GTX 1650 Ti, apparently OpenGL

### Issue description

When creating a new project, the editor window freezes:


There is nothing of note in the console log, from what I can tell; the first two warnings are because I'm using the NuGet version, where the EXE filename isn't case-matching.

```
WARNING: Case mismatch opening requested file 'godot_v4.2.1-stable_win64.exe', stored as 'Godot_v4.2.1-stable_win64.exe.
at: open_internal (drivers/windows/file_access_windows.cpp:132)
WARNING: Case mismatch opening requested file 'godot_v4.2.1-stable_win64.exe', stored as 'Godot_v4.2.1-stable_win64.exe.
at: open_internal (drivers/windows/file_access_windows.cpp:132)
Godot Engine v4.2.1.stable.official.b09f793f5 - https://godotengine.org
OpenGL API 3.3.0 NVIDIA 532.09 - Compatibility - Using Device: NVIDIA - NVIDIA GeForce GTX 1650 Ti

Project is missing: c:/temp/audiotest/project.godot
```

### Steps to reproduce

- Set up your laptop with an external monitor, and Windows set to "Extend display"
- Open Godot
- Move Godot to the monitor screen
- Click the new project button
- Wait. Forever.

Note that creating a project on the first/default (laptop/internal) screen works fine.

### Minimal reproduction project (MRP)

Not applicable.

Start by reproducing the freeze using the reported Windows extended-display steps: move Godot to the external monitor and use the New Project button. Check the editor's new-project flow and the related window handling; done means creating a project works on the second screen without freezing while the first-screen behavior remains intact.

Written by the indexing model from the issue text.