Keep MCP user interaction on the root thread (#46066)

## Why

MCP requests that need human input, including browser sign-in, must be handled by the root thread. Subagents need guidance to hand these blockers to their parent without prompting the user or automatically accepting requests that require input.

## What changed

- Reject interactive MCP elicitations and tool approval prompts in subagents with guidance to ask the parent and wait before retrying.
- Recognize browser authentication and `codex_requires_user_input` metadata even when the form schema is empty, while preserving automatic permission approvals and review decisions.
- Carry user-interaction eligibility through MCP runtime creation and connection reuse, and guard prompt registration.
- Preserve connector authentication diagnostics alongside handoff guidance, subject to normal tool-output limits.

## Testing

Add unit and integration coverage for blocked subagent prompts, root browser authentication, automatic approval and review, connection reuse, and authentication diagnostic preservation and truncation. Add a request-history snapshot for browser-auth handoff guidance.

GitOrigin-RevId: 83e146b6e5c1a2a22a34681ad45615f504b3c96c

codex-rs/app-server/src/request_processors/apps_processor/installed.rs

@@ -113,6 +113,7 @@ impl AppsRequestProcessor {
                         client_mcp_extensions: ClientMcpExtensions::default(),
                         auth: auth.clone(),
                         auth_manager: codex_apps_auth_manager,
+                        allow_user_interaction: true,
                         elicitation_reviewer: None,
                         elicitation_lifecycle: None,
                     })