Enable "autopilot" in settings to always start the session in that mode

### Feature summary

Enable "autopilot" in settings to always start the session in that mode

### What problem are you trying to solve?

I now have to select autopilot in every session, especially now that the interactive mode does not create a PR by default, it becomes rather tedious.

### Proposed solution

Add a setting to use a default mode for new sessions.

### Workflow impact

High, it is extra clicking for every session

### Installation context

_No response_

### Additional context

_No response_

Start by tracing the settings UI and the code that chooses the mode for a new session. Add a persistent default-mode setting for autopilot and verify that new sessions use it without requiring an extra selection.

Written by the indexing model from the issue text.