Scene takes ~10 seconds longer on startup if another Godot Instance or the Godot Project Manager is open in the background

### Tested versions

Godot v4.3.stable (77dcf97d8)

### System information

Godot v4.3.stable (77dcf97d8) - Windows 10.0.19045 - Vulkan (Forward+) - dedicated NVIDIA GeForce RTX 3070 Laptop GPU (NVIDIA; 32.0.15.6614) - 11th Gen Intel(R) Core(TM) i7-11800H @ 2.30GHz (16 Threads)

### Issue description

If the project manager is open, starting the main or a custom scene takes an extra 10 seconds.

Here is a comparison video:
Left shows me running a project.
Right, starting the same project but the project manager is also open in the background

https://github.com/user-attachments/assets/168d5940-d833-450a-a49b-44c36d31f405

This is the same if another Instance of the Godot Editor is open in the background. But I found it interesting that the project manager already causes this issue.

### Steps to reproduce

Open a Godot Project.
Open a new Godot Project manager.
Run your project.

### Minimal reproduction project (MRP)

N/A

Reproduce the delay using the listed steps on Windows 10, comparing startup with and without another Godot Project Manager or editor instance open. Measure the scene startup time in both cases and trace the startup path to identify where the extra delay occurs; done means the reported additional delay is eliminated without regressing normal startup.

Written by the indexing model from the issue text.