[BUG] Custom skills from "My Skills" not available to agent on web version

Preflight Checklist

• [x] I have searched existing issues 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?

Custom skills created in "My Skills" are not accessible to the agent on the web/app version of Claude Code. The skill appears in the UI but the agent cannot invoke it. The same skills work correctly on the CLI version.

What Should Happen?

Custom skills should be available to the agent on the web version, consistent with CLI behavior. When a user creates a skill, the agent should be able to invoke it via the Skill tool.

Error Messages/Logs

No error is thrown. The agent simply does not list custom skills among its available skills. Only built-in skills appear (keybindings-help, simplify, loop, claude-api, session-start-hook).

Steps to Reproduce

1. Create a custom skill in "My Skills" (e.g., git-commit)
2. Open a session on the web version of Claude Code
3. Ask the agent to use the custom skill or invoke it with /git-commit
4. Agent reports the skill is not available

Note: This works correctly on the CLI version.

Claude Model

Opus

Is this a regression?

I don't know

Last Working Version

_No response_

Claude Code Version

2.1.76

Platform

Anthropic API

Operating System

macOS

Terminal/Shell

Terminal.app (macOS)

Additional Information

This makes the "My Skills" feature unusable on the web version. Users can create skills but the agent has no way to access them, which defeats the purpose of the feature.