AudioStreamInteractive does not auto-advance from clip switched to using switch_to_clip_by_name

### Tested versions

- v4.6.2.stable.nixpkgs [001aa128b]
- v4.5.1.stable.nixpkgs [f62fdbde1]
- v4.4.1.stable.nixpkgs [49a5bc7b6]

### System information

Godot v4.6.2.stable (001aa128b) - cpe:/o:nixos:nixos:26.05 #1-NixOS SMP PREEMPT_DYNAMIC Wed Apr 22 11:22:34 UTC 2026 on Wayland - X11 display driver, Multi-window, 1 monitor - Vulkan (Forward+) - dedicated NVIDIA GeForce RTX 3050 Laptop GPU - AMD Ryzen 5 4600H with Radeon Graphics (12 threads) - 15.04 GiB memory

### Issue description

The setup is a simple case of transitioning to a chorus after playing a filler clip, triggered by pressing a button.
The chorus clip is set to auto-advance to the initial "main" clip, but when done, it does not do so.

### Steps to reproduce

Run the project and press the button once. The transition will begin on the next beat.

### Minimal reproduction project (MRP)

[godot_audio_2026-05-12_16-38-5021.zip](https://github.com/user-attachments/files/27643064/godot_audio_2026-05-12_16-38-5021.zip)

Start by running the attached minimal reproduction project and pressing the button once to observe the transition. Then trace AudioStreamInteractive handling of switch_to_clip_by_name and the chorus clip's auto-advance setting. Done means the chorus returns to the initial main clip after playback completes, with the reproduction behavior covered by an appropriate test.

Written by the indexing model from the issue text.