feat(app): display worktree slug in tab headers

[jadelike-wine]

feat(app): display worktree slug in tab headers

Show the worktree slug (basename of workspace path) as a muted secondary label alongside the branch/agent name across the UI:

• Add extractWorktreeSlug() and shouldShowWorktreeSlug() utilities
• Sidebar workspace list: show slug under branch name
• Agent list: show slug in meta row (mobile) and column (desktop)
• Workspace header: show slug below the title bar
• Tab headers: show slug next to agent title in tab chip and option row
• Add worktreeSlug to PanelDescriptor and thread through resolver
• Add tests for slug extraction and sidebar/workspace integration

Closes #1008

Linked issue

Closes #1008

Type of change

• New feature (with prior issue + design alignment)

What does this PR do

Show the worktree slug (basename of workspace path) as a muted secondary label alongside the branch/agent name across the UI. Previously the UI only showed the branch name, making it hard to identify which Docker container or external tool to point at for a given worktree.

Changes:

• Add extractWorktreeSlug() and shouldShowWorktreeSlug() shared utilities that parse the canonical $PASEO_HOME/worktrees/<hash>/<slug> path pattern
• Sidebar workspace list: show slug under the branch name
• Agent list: show slug in meta row (mobile) and column (desktop)
• Workspace header: show slug below the title bar
• Tab headers: show slug next to the agent title in both the tab chip and the dropdown option row
• Add worktreeSlug to PanelDescriptor and thread it through the WorkspaceTabPresentation resolver
• Add tests for slug extraction and sidebar/workspace integration

How did you verify it

• npm run typecheck — passes across all workspaces
• npm run lint — 0 errors, 0 warnings
• npm run format — all files formatted
• Manual review of the diff for correctness

Checklist

• One focused change. Unrelated cleanups split out.
• npm run typecheck passes
• npm run lint passes
• npm run format ran (Biome)
• UI changes include screenshots or video for every affected platform
• Tests added or updated where it made sense