Describe the bug

Any interaction with the tab bar or split pane layout that affects the currently active tab causes the terminal session inside it to be refreshed or killed outright. This makes split pane workflows nearly unusable if you have a running process (dev server, build, etc.) in a terminal tab.

Steps to reproduce

1. Open a terminal tab and start a long-running process (e.g. npm run dev)
2. Attempt any of the following:
   • Create a new split pane
   • Move the current tab
   • Switch to another tab and back
3. The terminal session in the original tab is killed or reset

Expected behavior

Tab layout changes and split operations should be non-destructive. Terminal sessions should persist independently of tab arrangement, exactly like they do in VS Code, Zed, or any standard terminal multiplexer.

Notes

This is likely a component unmount/remount issue. When the tab layout re-renders after a structural change, the terminal component is probably being fully unmounted rather than preserved. Keeping terminal instances alive in a separate process tree or using a keyed approach that prevents remounting would fix this. Worth looking at how the terminal is mounted relative to the tab panel component lifecycle.