Show worktree names in workspace hover cards (#2711)

* fix(app): show worktree names in workspace hover cards

Managed worktree paths exposed Paseo's internal directory layout instead of the useful worktree name. Carry the owned worktree root through the sidebar model while preserving the full workspace path as the copy target.

* fix(workspaces): source owned worktree names from daemon

The daemon owns worktree path semantics, so expose the managed worktree slug and let the sidebar model produce a display-ready label. This keeps path parsing out of the hover-card component while preserving the full path for copying.

* fix(app): preserve worktree labels in replica cache

packages/server/src/server/session.ts

@@ -1,7 +1,7 @@
 import equal from "fast-deep-equal";
 import { v4 as uuidv4 } from "uuid";
 import { lstat, mkdir, mkdtemp, rename, rm, stat } from "node:fs/promises";
-import { resolve, sep } from "path";
+import { basename, resolve, sep } from "path";
 import { homedir } from "node:os";
 import { CLIENT_CAPS, type ClientCapability } from "@getpaseo/protocol/client-capabilities";
 import {
@@ -4276,6 +4276,11 @@ export class Session {
       diffStat = snapshot.git.diffStat;
     }
 
+    const worktreeSlug =
+      workspace.isPaseoOwnedWorktree && workspace.worktreeRoot
+        ? basename(workspace.worktreeRoot)
+        : undefined;
+
     return {
       id: workspace.workspaceId,
       projectId: workspace.projectId,
@@ -4286,6 +4291,7 @@ export class Session {
       projectCustomIconRevision: resolvedProjectRecord?.customIconRevision ?? null,
       projectRootPath: resolvedProjectRecord?.rootPath ?? workspace.cwd,
       workspaceDirectory: workspace.cwd,
+      worktreeSlug,
       projectKind: (resolvedProjectRecord?.kind ?? "directory") === "git" ? "git" : "non_git",
       workspaceKind: workspace.kind,
       name: resolveWorkspaceDisplayName(workspace),
@@ -4373,6 +4379,7 @@ export class Session {
       projectCustomIconRevision: projectRecord?.customIconRevision ?? null,
       projectRootPath: projectRecord?.rootPath ?? result.repoRoot,
       workspaceDirectory: result.workspace.cwd,
+      worktreeSlug: basename(result.worktree.worktreePath),
       projectKind: projectRecord?.kind ?? "git",
       workspaceKind: result.workspace.kind,
       name: resolveWorkspaceName({