Windows: app window is always-on-top with no way to disable it

## Summary

The Claude Code desktop app window stays above all other windows. There is no setting, shortcut, or menu item to turn this off.

## Environment

- Claude Code 2.1.138 (desktop app)
- Windows 10 Pro 22H2 (10.0.19045)

## Steps to reproduce

1. Open the Claude Code desktop app
2. Open any other window (browser, editor, file explorer)
3. Click that window, or Alt+Tab to it

**Expected:** the other window comes to the front.

**Actual:** it takes keyboard focus but renders *behind* the Claude Code window, which stays on top.

## Why this matters

It makes ordinary side-by-side work impractical — reading documentation in a browser while working in Claude Code, or copying between the two. The app cannot be used as one window among several.

## What I checked before filing

- No `alwaysOnTop` key in `~/.claude/settings.json`
- No window or appearance toggle in the app
- No documented keyboard shortcut

## Workaround

Windows virtual desktops (`Win+Ctrl+D`), which works because "always on top" is per-desktop. Minimising the window also works but is not practical for frequent switching.

## Related issues (both closed, neither fixed)

- #87895 (Windows) — closed as a duplicate of #66516
- #66516 (macOS) — closed as "not planned" / "invalid"

#87895 was closed as a duplicate of an issue that had itself been closed as not-planned, so this looks like it fell between the two rather than having been declined on merit. It still reproduces on 2.1.138.

The payload names no source files, tests, or entry points. Start by reproducing the behavior on Windows 10 and locating the desktop window initialization and focus handling; then trace how the always-on-top state is set. Done means another window can be brought in front while Claude Code remains open, with a supported way to disable the behavior and a regression check.

Written by the indexing model from the issue text.