[FEATURE] Folder picker should show trailing path segments instead of truncating them

Problem Statement

In Claude Desktop (Windows), the folder picker truncates long paths from the right, hiding the most distinguishing part. For users whose projects live in deep directory structures (e.g., OneDrive-synced folders with per-client/per-project nesting), the visible portion is identical across all entries — only the common prefix shows.

For example, paths like these all look the same in the picker:

C:\Users\Name\OneDrive - Company\Documents\Clients\ClientA\004 - Project Alpha...
C:\Users\Name\OneDrive - Company\Documents\Clients\ClientA\005 - Project Beta...
C:\Users\Name\OneDrive - Company\Documents\Clients\ClientB\001 - Project Gamma...

The client name and project number — the only distinguishing info — are cut off or barely visible.

Proposed Solution

Show the last 2–3 path segments prominently (e.g., ClientA\004 - Project Alpha) with the leading path abbreviated or shown in a muted style. VS Code's tab labels and breadcrumbs are a good reference for this pattern.

Alternative Solutions

Workarounds include Windows SUBST drives or symlinks to shorten the base path, but these add indirection that can confuse OneDrive sync, git, and other tools.

Use Case Example

1. I work with 20+ project folders under a deeply nested OneDrive-synced path
2. I open Claude Desktop and click the folder picker to switch projects
3. Every entry shows the same long shared prefix, truncating the distinguishing tail
4. I can't tell which project is which without hovering or memorizing order
5. With tail-segment display, I'd immediately see ClientA\004 - Project Alpha and pick the right one