[BUG] SendUserFile: "Save skill" button missing on .skill files

### 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?

When Claude delivers .skill files via the SendUserFile tool, the file cards appear with the SKILL badge, filename, and size — but no "Save skill" button is shown. There is no way to install the skill from the UI.

### What Should Happen?

A "Save skill" button should appear on .skill file cards delivered via SendUserFile, allowing the user to install the skill into their profile directly from the conversation

### Error Messages/Logs

```shell

```

### Steps to Reproduce

1. Use the skill-creator skill to package a custom skill via package_skill.py
2. Claude delivers the .skill file via SendUserFile
3. The file card appears with the SKILL badge, filename, and file size
4. No "Save skill" button is visible — card is display-only

### Claude Model

Sonnet (default)

### Is this a regression?

I don't know

### Last Working Version

_No response_

### Claude Code Version

2.1.177 (Claude Code)

### Platform

Other

### Operating System

macOS

### Terminal/Shell

Terminal.app (macOS)

### Additional Information

Start at the SendUserFile handling and the file-card rendering described in the report; package_skill.py is the only file entry point mentioned. Trace how .skill files are identified and how their card actions are chosen. Done means a delivered .skill card shows a working “Save skill” action and the existing reproduction flow confirms installation is available.

Written by the indexing model from the issue text.