[codex] Improve workspace runtime and navigation ergonomics (#3680)

## Thinking Path

> - Paperclip orchestrates AI agents for zero-human companies
> - That operator experience depends not just on issue chat, but also on
how workspaces, inbox groups, and navigation state behave over
long-running sessions
> - The current branch included a separate cluster of workspace-runtime
controls, inbox grouping, sidebar ordering, and worktree lifecycle fixes
> - Those changes cross server, shared contracts, database state, and UI
navigation, but they still form one coherent operator workflow area
> - This pull request isolates the workspace/runtime and navigation
ergonomics work into one standalone branch
> - The benefit is better workspace recovery and navigation persistence
without forcing reviewers through the unrelated issue-detail/chat work

## What Changed

- Improved execution workspace and project workspace controls, request
wiring, layout, and JSON editor ergonomics
- Hardened linked worktree reuse/startup behavior and documented the
`worktree repair` flow for recovering linked worktrees safely
- Added inbox workspace grouping, mobile collapse, archive undo,
keyboard navigation, shared group-header styling, and persisted
collapsed-group behavior
- Added persistent sidebar order preferences with the supporting DB
migration, shared/server contracts, routes, services, hooks, and UI
integration
- Scoped issue-list preferences by context and added targeted UI/server
tests for workspace controls, inbox behavior, sidebar preferences, and
worktree validation

## Verification

- `pnpm vitest run
server/src/__tests__/sidebar-preferences-routes.test.ts
ui/src/pages/Inbox.test.tsx
ui/src/components/ProjectWorkspaceSummaryCard.test.tsx
ui/src/components/WorkspaceRuntimeControls.test.tsx
ui/src/api/workspace-runtime-control.test.ts`
- `server/src/__tests__/workspace-runtime.test.ts` was attempted, but
the embedded Postgres suite self-skipped/hung on this host after
reporting an init-script issue, so it is not counted as a local pass
here

## Risks

- Medium: this branch includes migration-backed preference storage plus
worktree/runtime behavior, so merge review should pay attention to state
persistence and worktree recovery semantics
- The sidebar preference migration is standalone, but it should still be
watched for conflicts if another migration lands first

## Model Used

- OpenAI Codex coding agent (GPT-5-class runtime in Codex CLI; exact
deployed model ID is not exposed in this environment), reasoning
enabled, tool use and local code execution enabled

## Checklist

- [x] I have included a thinking path that traces from project context
to this change
- [x] I have specified the model used (with version and capability
details)
- [ ] I have run tests locally and they pass
- [x] I have added or updated tests where applicable
- [ ] If this change affects the UI, I have included before/after
screenshots
- [x] I have updated relevant documentation to reflect my changes
- [x] I have considered and documented any risks above
- [x] I will address all Greptile and reviewer comments before
requesting merge

---------

Co-authored-by: Paperclip <noreply@paperclip.ing>

ui/src/pages/Inbox.test.tsx

@@ -5,7 +5,7 @@ import type { ComponentProps } from "react";
 import { createRoot } from "react-dom/client";
 import type { Issue } from "@paperclipai/shared";
 import { afterEach, beforeEach, describe, expect, it, vi } from "vitest";
-import { FailedRunInboxRow, InboxIssueMetaLeading, InboxIssueTrailingColumns } from "./Inbox";
+import { FailedRunInboxRow, InboxGroupHeader, InboxIssueMetaLeading, InboxIssueTrailingColumns } from "./Inbox";
 
 vi.mock("@/lib/router", () => ({
   Link: ({ children, className, ...props }: ComponentProps<"a">) => (
@@ -245,3 +245,52 @@ describe("InboxIssueTrailingColumns", () => {
     });
   });
 });
+
+describe("InboxGroupHeader", () => {
+  let container: HTMLDivElement;
+
+  beforeEach(() => {
+    container = document.createElement("div");
+    document.body.appendChild(container);
+  });
+
+  afterEach(() => {
+    container.remove();
+  });
+
+  it("shows a left caret and expanded state for collapsible mobile headers", () => {
+    const root = createRoot(container);
+
+    act(() => {
+      root.render(<InboxGroupHeader label="Primary workspace (default)" collapsible collapsed={false} />);
+    });
+
+    const button = container.querySelector("button");
+    expect(button).not.toBeNull();
+    expect(button?.getAttribute("aria-expanded")).toBe("true");
+    expect(button?.textContent).toContain("Primary workspace (default)");
+    const caret = container.querySelector("svg");
+    expect(caret?.className.baseVal).toContain("rotate-90");
+
+    act(() => {
+      root.unmount();
+    });
+  });
+
+  it("keeps the caret collapsed when the mobile group is hidden", () => {
+    const root = createRoot(container);
+
+    act(() => {
+      root.render(<InboxGroupHeader label="Feature Branch" collapsible collapsed />);
+    });
+
+    const button = container.querySelector("button");
+    expect(button?.getAttribute("aria-expanded")).toBe("false");
+    const caret = container.querySelector("svg");
+    expect(caret?.className.baseVal).not.toContain("rotate-90");
+
+    act(() => {
+      root.unmount();
+    });
+  });
+});