aws login: stale browser cookies cause 400 Bad Request — CLI hangs until timeout with no feedback

### Describe the bug

When `aws login` opens the browser and stale AWS session cookies are present, the signin
portal returns `400 Bad Request` directly to the browser. The CLI's local callback server
(`127.0.0.1:PORT`) never receives a redirect, so the process hangs silently for up to
10 minutes with no feedback before failing.

### Expected Behavior

When a browser session cookie is detected but the underlying session has expired, the
server should redirect the browser to the login page so the user can re-authenticate and
complete the OAuth flow naturally — rather than returning 400.

If redirecting to the login page is not possible, the server should communicate the failure
back through the `redirect_uri` with an `error` parameter as required by
[RFC 6749 §4.1.2.1](https://datatracker.ietf.org/doc/html/rfc6749#section-4.1.2.1),
allowing the CLI to surface a meaningful error immediately.

### Current Behavior

1. CLI starts a local callback server at `http://127.0.0.1:PORT/oauth/callback`
2. CLI opens `/v1/authorize?...&redirect_uri=http://127.0.0.1:PORT/oauth/callback` in the browser
3. The server detects existing browser session cookies and attempts to reuse the session
4. Browser is redirected to `/v1/sessions?...`
5. Browser is redirected to `/oauth?iam_user=true&backwards_compatible=true&...`
6. Server returns **400 Bad Request** — browser shows an error page and stops
7. The `redirect_uri` is never called; the CLI hangs for up to 10 minutes then raises
`PendingAuthorizationExpiredError` with no useful message

### Reproduction Steps

1. Sign into the AWS Management Console in your browser (sets session cookies)
2. Wait for the server-side session to expire (the browser cookies remain)
3. Run `aws login`
4. The browser opens and immediately shows a 400 error page
5. The CLI prints nothing — it hangs until the 10-minute `_OVERALL_TIMEOUT` in
`AuthCodeFetcher.get_auth_code_and_state()`, then raises `PendingAuthorizationExpiredError`

### Possible Solution

Replace the current error-based stale cookie handling with a proper authentication redirect flow. Instead of surfacing a 400 error to the user when a stale cookie is detected, the server should transparently redirect the user through the login page so the CLI can obtain a fresh token without requiring manual intervention.
Current flow (broken):
**stale cookie detected → try session reuse → error 400**
Proposed flow:
**stale cookie detected → redirect to login page → user authenticates → redirect_uri called with auth code → CLI exchanges code for token**

### CLI version used

aws-cli/2.34.23

### Environment details (OS name and version, etc.)

Python/3.14.3 Linux/6.8.0-106-generic exe/x86_64.ubuntu.24 OS: Ubuntu 24.04 Browser: Brave (Chromium-based) Region: eu-south-2