Show worktree / workspace picker in more agent scenarios

[bamurtaugh]

I'm thinking of a couple aspects here for different agent harnesses.

Copilot CLI:
For non-git projects, the worktree / workspace picker is not shown (since the only option is inherently workspace for such projects). For consistency (since we're aiming to show as consistent of a set of dropdowns across agent and repo types as possible), should we show this picker, just with worktree grayed out (and/or some other explanation)? This could also help with discoverability (so that users know the option exists for git repos, if they choose to publish their repo to git, or work on another git-based repo)?

Local and Claude Agent:
Would we want to consider showing the worktree / workspace picker for non-CLI agent harnesses? I think this could make sense and aligns with what @TylerLeonhardt @rebornix and I discussed briefly last week about broadening certain paradigms to apply to any agent harness.

[TylerLeonhardt]

Steps:

• pull out the workspace/worktree picker from Copilot CLI integration to make it generic
• Add Option in Claude
• Adopt generic "cwd resolver" in Claude

That first step, @DonJayamanne said it's mostly generic... but probably needs a bit of work to make it truly generic and pulled out.

[DonJayamanne]

pull out the workspace/worktree picker from Copilot CLI integration to make it generic

The picker is definitely not generic
However the code users to create worktrees and manage those (committing, digging) are
However there is also the integration code

I think you already started using some of the code by creating subclasses