Startup banner suggests installing IDE plugin even when already installed

Description

When launching Claude Code from within WebStorm (with the JetBrains plugin already installed), the startup banner still displays:

↑ Install the WebStorm plugin from the JetBrains Marketplace: https://docs.claude.com/s/claude-code-jetbrains

This is confusing — the user is clearly already using the plugin since they're running Claude Code inside WebStorm's integrated terminal.

Expected behavior

The startup tip should either:

• Detect that the plugin is already installed and suppress the message
• Or at minimum, detect that Claude Code is running inside a JetBrains IDE terminal and skip the suggestion

Environment

• Claude Code v2.1.76
• WebStorm with Claude Code JetBrains plugin installed
• macOS