OAuth login times out after 15 seconds — not enough time for browser-based auth flow

Problem

The claude auth login command times out after 15 seconds if the user doesn't click Authorize in the browser fast enough. The browser page itself takes a few seconds to load, leaving very little time to actually authorize.

Behavior

1. Run claude auth login in Terminal
2. Browser opens to claude.ai authorization page
3. Page loads (takes 2-4 seconds)
4. User clicks Authorize
5. CLI returns: Login failed: Timeout of 15000 milliseconds exceeded

Expected behavior

The 15-second window should start AFTER the page has loaded and the user has had a reasonable opportunity to interact with it — or the timeout should be extended (30-60 seconds minimum).

Impact

Users end up in a frustrating loop where login repeatedly fails with no clear indication that the fix is simply to click faster. The error message does not explain the timeout or suggest retrying quickly.