Closes AI-403

Recently, we introduced the ability to pick, from the plus icon button
in a project's header in the sidebar, which of the currently loaded
worktree you'd like to create a new thread on. This PR extends this
ability by allowing you to _create_ a new worktree from there as well.
Turned out this just felt like a natural move after playing around with
the change internally; we had a good amount of internal asks for this.
What's exposed in the menu is exactly the same options available in the
worktree picker, following the same display rules.

<img width="650" alt="Screenshot 2026-06-15 at 12  22@2x"
src="https://github.com/user-attachments/assets/ef45d93e-9106-46c6-9a8b-bc099036a7de"
/>

Release Notes:

- Agent: Enabled creating a new worktree from the sidebar's "new thread"
icon button.