Noticeable freeze after saving a scene

[KoBeWi]

Tested versions

Regression from #77932

System information

Windows 10.0.19045 - Vulkan (Forward+) - dedicated NVIDIA GeForce GTX 1060 (NVIDIA; 31.0.15.4633) - Intel(R) Core(TM) i7-7700HQ CPU @ 2.80GHz (8 Threads)

Issue description

I noticed that there is a noticeable editor freeze when saving a scene. I did some profiling and it turns out that when you save a scene, it causes EditorFileSystem update, which causes the FileSystem dock to... reload the whole tree.

While previously it wouldn't be that noticeble, it is after #77932.

Here's a comparison in a dev build.
With #77932

godot.windows.editor.dev.x86_64_tpRpT69keo.mp4

Without #77932

godot.windows.editor.dev.x86_64_nZFpWFZHIC.mp4

It's 3 times shorter. Maybe we wouldn't have freeze at all if the FileSystem dock did not decide to update for no reason.

Steps to reproduce

1. Open a project with many resources (e.g. 2000)
2. Save a scene

Minimal reproduction project (MRP)

N/A