AnimationTree, StateMachine, inspector update requires deselect and selected

### Tested versions

Reproducible in: v4.7.beta1.official [1c8cc9e7e], v4.6.2.stable.official [71f334935]

### System information

Godot v4.7.beta1 - Windows 11 (build 26100) - Multi-window, 1 monitor - OpenGL 3 (Compatibility) - GeForce GTX 550 Ti - Intel(R) Core(TM) i3-2100 CPU @ 3.10GHz (4 threads) - 11.95 GiB memory - WASAPI (48000 Hz, Stereo/mono)

### Issue description

The inspector doesn't update when selecting a selected StateMachine node in the AnimationTree panel.

The inspector updates to show the StateMachine's properties when the StateMachine node is deselected then selected again.

Video description:
The AnimationTree node is selected in the scene panel.
The mouse moves over the inspector, to indicate that it's showing the AnimationTree's properties.

The StateMachine is selected in the AnimationTree panel.
The mouse moves over the inspector, to indicate that it's showing the StateMachine's properties.

The AnimationTree node is selected in the scene panel.
The mouse moves over the inspector, to indicate that it's showing the AnimationTree's properties.

The selected StateMachine is clicked multiple times in the AnimationTree panel, but the inspector doesn't change from showing the AnimationTree's properties to showing the StateMachine's properties.

The mouse clicks outside the StateMachine node to deselect it.
The mouse clicks on the StateMachine node to select it again.
Now the inspector shows the StateMachine's properties.

End of video.

https://github.com/user-attachments/assets/5aacde53-df67-4956-bba1-d60661c5fdac

### Steps to reproduce

- open the project: [inspector-doesn't-update-when-selecting-statemachine.zip](https://github.com/user-attachments/files/27393213/inspector-doesn.t-update-when-selecting-statemachine.zip)- in the scene panel, click on the AnimationTree
note: the inspector shows the AnimationTree's properties
- in 4.6.2.stable, the bottom Animation panel opens, click on the bottom AnimationTree button
- in the bottom AnimationTree panel, in the bottom right minimap
- drag the light gray rectangle (the visible area), to the black rectangles on the minimap (the StateMachine and Output nodes)
- select the StateMachine node
note: the inspector shows the StateMachine's properties
- in the scene panel, click on the AnimationTree
note: the inspector shows the AnimationTree's properties
- in the bottom AnimationTree panel, select the already selected StateMachine node

Issue:
The inspector still shows the AnimationTree's properties, it didn't update to show the StateMachine's properties.

The inspector only shows the StateMachine node's properties when the StateMachine node is deselected then selected again.

Expected:
Update the inspector to show the StateMachine's properties when it's clicked, without having to deselect it first.

### Minimal reproduction project (MRP)

[inspector-doesn't-update-when-selecting-statemachine.zip](https://github.com/user-attachments/files/27393213/inspector-doesn.t-update-when-selecting-statemachine.zip)

Open the linked minimal reproduction project in Godot 4.6.2 or 4.7.beta1 and follow the AnimationTree panel steps, focusing on StateMachine selection and the Inspector update. Trace the AnimationTree panel's selection handling and verify that clicking an already selected StateMachine updates the Inspector without requiring deselection.

Written by the indexing model from the issue text.