Scene tab bar scroll position resets when closing a tab with middle click

### Tested versions

- Reproducible in 4.4-stable and v4.5.dev.custom_build [c3ae6aa10]

### System information

Godot v4.4.stable - Linux Mint 22.1 (Xia) on X11 - X11 display driver, Multi-window, 3 monitors - Vulkan (Forward+) - dedicated NVIDIA GeForce RTX 2080 Ti (nvidia; 570.133.07) - AMD Ryzen 9 3900X 12-Core Processor (24 threads)

### Issue description

If you have a lot of tabs open and try to close a few of them with middle click to fight the clutter the bar will repeatedly reset position to the far right edge.

https://github.com/user-attachments/assets/3d2fce0b-6047-4a94-b657-18cf4d7d4db3

### Steps to reproduce

- Open so many tabs that you can scroll on the scene tab bar.
- Scroll to the left side and close a tab using middle click.
- Observe that the bar position has teleported.

### Minimal reproduction project (MRP)

[Here's a project with a bunch of empty scenes with long names](https://github.com/user-attachments/files/20492533/tab-bar-issue.zip)