[Bug] Harness Browser: Live View "Take control"/"Release" breaks the agent's automation on SSO handback (workaround: interact without Take control + reconnect)

## Summary (corrected after further testing)

On a **managed AgentCore Harness** with the built-in **Browser** tool, you can let a human complete an interactive **SSO login** (e.g. IAM Identity Center / a federated QuickSight console where the OTP arrives by email) in **Live View** and then have the agent continue in the **same authenticated session** — **but only if you avoid the Live View "Take control" / "Release control" toggle.**

- **Broken path:** human clicks **Take control**, completes the SSO+OTP login, clicks **Release control**, then the agent resumes. → The agent's automation context is destroyed. Every subsequent automation call returns `Target page, context or browser has been closed`, and shortly after the backend reports it is gone (`not initialized` / "all sessions are gone"). The authenticated session is unrecoverable. Reproduced across 3 orchestration strategies (concurrent polling, blind hands-off, signal-gated hands-off where the agent provably never touched the browser during the human's control).
- **Working path (workaround):** human interacts in Live View **without** clicking Take control (types the OTP / completes login directly), then the agent, on resume, **does NOT reuse its pre-login page handle** — it **reconnects / re-reads the current page** (e.g. via `evaluate` / re-navigate). → The authenticated state **carries over**; the agent lands on the authenticated console and proceeds normally. Verified end to end against a real QuickSight Enterprise console.

So the issue is specifically: **the documented Live View take-over/release-control feature does not cleanly hand control back to the managed-harness agent's automation** (it tears down the automation context), even though the dev guide presents take/release control as a feature ("interactive controls to take over or release control from automation").

## Environment

- boto3 `1.43.29` (`bedrock-agentcore-control` + `bedrock-agentcore`), managed Harness (`CreateHarness`/`InvokeHarness`), browser `aws.browser.v1`, `networkMode: PUBLIC`, region `us-east-1`.
- Tools: `agentcore_browser` + `agentcore_code_interpreter` + inline functions; `allowedTools: ["*"]`.

## Repro (both paths)

1. Harness with `agentcore_browser`; invoke a task that navigates to an SSO-gated console URL. Agent lands on the sign-in page (expected).
2. Open the session's Live View.
- **(broken)** Click **Take control** → complete SSO+OTP → **Release control** → agent resumes → context dead.
- **(works)** Do **not** click Take control; complete the login directly in the stream → then the agent **reconnects** (re-reads the page rather than reusing the old handle) → authenticated session carries over.

## Asks

1. Is the **Take control → Release control** path *intended* to hand control back to the harness agent's automation? If so, the teardown is a bug; if not, please document that interacting **without** Take control (plus an automation reconnect) is the supported human-assisted-auth pattern.
2. Could the automation context **survive** a take/release cycle so the documented feature works for the managed harness?
3. Separately: the harness `agentcore_browser` tool config only accepts `browserArn` (no `profileConfiguration`), so a pre-saved authenticated browser profile cannot be attached as an alternative to interactive login. A `profileConfiguration` passthrough would help.

Happy to share CloudWatch DEFAULT-log-group traces for both the broken and working runs.

Beginne damit, die beiden Live View-Pfade mit dem verwalteten Harness, agentcore_browser und einem SSO-Ablauf zu reproduzieren, und vergleiche anschließend die Traces der CloudWatch DEFAULT-log-group. Untersuche die Übergabe zwischen take-control und release-control sowie das Verhalten beim Wiederverbinden der Sitzung. Als erledigt gilt die Aufgabe, wenn die Automatisierung den Zyklus übersteht oder der unterstützte Workaround und die Einschränkung von profileConfiguration klar dokumentiert sind.

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