[Feature Request] Use non-default VS Code terminal profile to run Claude Code

The Claude toolbar button and keyboard shortcut open Claude Code using the default terminal profile.

This can add to the time it takes to start Claude Code.

It also precludes having tmux as the default profile.

For this reason, I think it would be useful if users could configure Claude Code to open itself using a different profile.

For the keyboard shortcut (and not the Claude button) one can program this behavior by editing keybindings.json:

{
  "key": "cmd+escape",
  "command": "-claude-code.runClaude.keyboard",
  "when": "claude-code.hasClaudeInPath"
},
{
  "key": "cmd+escape",
  "command": "runCommands",
  "args": {
    "commands": [
      {
        "command": "workbench.action.terminal.newWithProfile",
        "args": {
          "profileName": "Claude"
        }
      },
      "workbench.action.newGroupRight",
      "workbench.action.terminal.moveToEditor",
    ]
  }
}

This keybinding uses to a claude terminal profile specified in settings.json which starts up faster than my default profile:

"Claude": {
  "overrideName": true,
  "path": "/bin/sh",
  "args": ["-c", "claude"],
  "icon": "robot"
}