No way to sign out / switch accounts in Claude in Chrome extension

Bug: No way to sign out / switch accounts in Claude in Chrome extension

Description

The Claude in Chrome extension has no sign-out or account-switching option. Once signed in, it keeps using that account's session even after removing and reinstalling the extension — there is no way to change which account it's logged in as short of clearing browser data at the OS/browser level.

This is inconsistent with the Claude Code CLI and desktop GUI, both of which allow logging out and choosing a different account.

Steps to reproduce

1. Install the Claude in Chrome extension and sign in with Account A's email.
2. Change/update the account email being used elsewhere (e.g., switch to a different email for Claude).
3. Try to sign out of the extension or switch accounts within the extension UI — there is no such option.
4. Remove the extension entirely and reinstall it.
5. The extension still loads the previous session/login (Account A), instead of prompting for a fresh sign-in.

Expected behavior

The extension should provide a visible "Sign out" / "Switch account" option in its panel, consistent with the Claude Code CLI (/logout or similar) and the desktop GUI, which both support logging out and choosing a different account.

Actual behavior

• No sign-out control exists anywhere in the extension UI.
• Removing and reinstalling the extension does not clear the stored session — it silently reloads the previous account's login.

Environment

• Browser: Chrome
• Extension: Claude in Chrome
• Platform: macOS (Darwin)

Impact

Users who need to switch Claude accounts (e.g., after an email change) are blocked from doing so in the browser extension, even though this is supported in other Claude Code surfaces (CLI, desktop GUI).