Moving tabs out of terminal doesn't work properly with startupActions, again

### Windows Terminal version

1.23.13503.0

### Windows build number

10.0.26200.7462

### Other Software

python 3.11 script

### Steps to reproduce

1. Open a python script that stays open (I'm using Java program and a python runner wrapper)
2. Drag that tab out
3. Randomly will open a new window as if i typed it into the start menu

### Expected Behavior

Tab that is dragged out should still be that tab and not a new Windows with default tabs

### Actual Behavior

Randomly acts like I opened a new window from the start menu and permanently losses the terminal instance

Begin by reproducing the drag-out behavior with Windows Terminal 1.23.13503.0, the listed Windows build, and a long-running Python or Java-backed process. Investigate how tab tear-out interacts with startupActions; done means the dragged tab consistently opens in its own window without losing the terminal instance or creating default tabs.

Written by the indexing model from the issue text.