[FEATURE] Desktop Code sidebar: show project folder next to session title when Group by: None

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

With Group by: None, sessions are listed by recency, which is the most useful
order — but there's no indication which project each session belongs to.
With 30+ projects, similar titles ("Status and roadmap", "General coding
session") become indistinguishable.

Proposed

• Show a short, muted project folder label next to (or under) each session title
• When space is tight, truncate the session title, not the label
• Clicking the label filters the list to that project

Why
A flat recency list with project labels answers "what was I just working on"
directly, without expanding groups or maintaining group order. Same pattern as
recent files in VS Code / JetBrains (filename + dimmed path).

Environment: Claude Desktop, macOS, Code tab

Proposed Solution

Show the project folder name next to each session title when Group by is set to None.

Either always, or behind a sidebar option "Show folder name" (in the same popover as Group by / Sort by).

Label rules:

• By default, show only the last segment of the session's working directory

(e.g. laconic for ~/src/laconic).

• If two or more listed sessions have working directories with the same last

segment but different paths, show the shortest path suffix that makes them
distinct (e.g. work/laconic vs personal/laconic), falling back to the
full path only if needed.

• The full path is always available in a tooltip on hover.
• The label is short and visually muted, so it doesn't compete with the title.
• When horizontal space is tight, truncate the session title first, not the label;

if the label itself must be shortened, truncate from the start, not the end,
so the distinguishing part stays visible.

Related: #83937 — turning grouping off restores a compact list, but then there is
no way to tell which project a session belongs to. This label addresses that.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Other

Use Case Example

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Additional Context

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