Opening project in editor fails with "Parse Error: Busy."

### Tested versions

- Reproducible in: v4.3.stable.official [77dcf97d8]

### System information

Godot v4.3.stable - Windows 10.0.22631 - Vulkan (Forward+) - integrated Intel(R) UHD Graphics (Intel Corporation; 31.0.101.4887) - 13th Gen Intel(R) Core(TM) i5-1345U (12 Threads)

### Issue description

The first time a project is opened in an editor (or after the .godot directory is removed), importing the scenes/scripts fails with:
```
ERROR: Parse Error: Busy. [Resource file res://thing.tscn:6]
at: _parse_node_tag (scene/resources/resource_format_text.cpp:289)
ERROR: Failed loading resource: res://thing.tscn. Make sure resources have been imported by opening the project in the editor at least once.
at: _load (core/io/resource_loader.cpp:283)
```

Closing and opening the same project a second time fixes the issue. The issue appears again if `.godot` directory is removed.

### Steps to reproduce

* Download and unzip the attached sample project.
* Make sure the project is not open in the Godot editor.
* `rm -rf .godot`
* `godot --editor --verbose --headless --import --quit`
* (Or open the project in the editor.)
* Observe the mentioned error in the output.

### Minimal reproduction project (MRP)

[repro2.zip](https://github.com/user-attachments/files/17203878/repro2.zip)