Unable to preview animations when both AnimationPlayer and AnimationTree are present

### Tested versions

reproducible in: 4.6, 4.6.1-rc1
not reproducible in: 4.5.1

### System information

Ubuntu 24.04

### Issue description

Unable to preview animations when both AnimationPlayer and AnimationTree nodes are present in the scene. Animation set in AnimationTree is preventing AnimationPlayer from showing/playing the animations from the library. The issue started after upgrade from 4.5 to 4.6.

### Steps to reproduce

1. Select AnimationTree node
2. Make sure in Bottom Panel the AnimationTree tab is selected
3. Now select AnimationPlayer node
4. Try to preview animations using the drop down menu - nothing happens

### Minimal reproduction project (MRP)

[MRP-AnimPlayer.zip](https://github.com/user-attachments/files/25348395/MRP-AnimPlayer.zip)