Continuing this work from a while back in #21079, now greatly aided by
agent + sonnet 4. With this change, there are now only a few spots that
explicitly panic, though errors during initialization will panic.

Motivation was this recent user panic in `handle_event`, figured fixing
all this use of unwrap was a great use of the agent.

> called `Result::unwrap()` on an `Err` value: X11 GetProperty for
_NET_WM_STATE failed.

Release Notes:

- N/A