[BUG] Floating Claude Code input widget overlaps/blocks the maximized editor panel (Problems/Output/Terminal/Ports/Comments)

### Preflight Checklist

- [x] I have searched [existing issues](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20state%3Aopen%20label%3Abug) and this hasn't been reported yet
- [x] This is a single bug report (please file separate reports for different bugs)
- [x] I am using the latest version of Claude Code

### What's Wrong?

### Environment
- **OS (host):** Windows 11 Pro 25H2 26200.8875
- **Remote:** WSL Ubuntu 24.04, connected via Remote-SSH
- **VS Code version:** 1.134.0
- **Claude Code extension version:** 2.1.260
- **Model in use:** Opus 5 (1M context)

### Description
The floating Claude Code input bar (the pill showing "ctrl esc to focus or unfocus Claude", the model selector, and the "Edit automatically" toggle) is rendered as an always-on-top overlay anchored to the editor area. It does not respect VS Code's native "Maximize Panel" layout state.

When the bottom panel (Problems / Output / Debug Console / Terminal / Ports / Comments) is maximized via the native VS Code command, this floating widget stays on screen and visually covers part of the maximized panel's content — in my case, several rows of the Problems tab (TypeScript/YAML diagnostics) were hidden behind it.

### What Should Happen?

### Expected Behavior
When a panel is maximized, it should either:
- fully cover/hide the floating Claude Code widget (as it does for regular editor content), or
- the widget should reposition/dock so it no longer overlaps panel content.

### Actual Behavior
The floating widget keeps its fixed position and z-index on top of the maximized panel, permanently occluding part of it. There is no obvious way to move or dismiss it without unfocusing Claude entirely (`Ctrl+Esc`).

#### Screenshot

### Workaround
- `Ctrl+Esc` to unfocus/collapse the Claude bar before maximizing the panel.
- Drag the panel to the Secondary Side Bar instead of maximizing it.
- Resize the panel manually instead of using "Maximize Panel".

### Additional Context
This only reproduces with the panel maximized; normal (non-maximized) panel layouts don't show the overlap since there's still editor space for the widget to occupy without covering panel content.

### Error Messages/Logs

```shell
### Screenshot

```

### Steps to Reproduce
1. Open a workspace with the Claude Code extension active (input bar visible/floating).
2. Open the bottom panel and select any tab (e.g. Problems).
3. Click "Maximize Panel" (or double-click the panel tab area) to expand it over the full editor region.
4. Observe that the Claude Code floating input bar remains on top of the maximized panel, obscuring part of its content.

### Claude Model

Opus

### Is this a regression?

I don't know

### Last Working Version

_No response_

### Claude Code Version

2.1.260

### Platform

Anthropic API

### Operating System

Ubuntu/Debian Linux

### Terminal/Shell

VS Code integrated terminal

### Additional Information

_No response_

No source file or test is named. Reproduce the issue in VS Code with the Claude Code input bar visible, then trace the floating widget's handling of the native Maximize Panel state; done means the widget is hidden or repositioned so it no longer obscures maximized panel content.

Written by the indexing model from the issue text.