Allow for local agents to be backgroundable

What would you like to be added?

Users should be able send local subagents to the background with Ctrl+B.

Why is this needed?

Frequently gemini-cli uses subagents for exploration or other non-blocking tasks like building and linting part of the codebase.

Additional context

As part of remote agents we have added PRs that would make this feature significantly easier to add with a shared injection and executionLifecycle class. See https://github.com/google-gemini/gemini-cli/issues/18197