Remove setTimeout from ArrowPanel

This is a follow-up to #1852.

The ArrowPanel has an animation, and some timing logic uses `setTimeout`. In review, Julien suggested:

> Also I think we can replace the whole dance you're doing with the setTimeout and the states with the react-transition-group library: there are these properties mountOnEnter and unmountOnExit that do exactly that.
> Not blocking this PR but doable as a follow-up. I think this would simplify this component a lot. But working with that library is sometimes frustrating when we're not used to it.

┆Issue is synchronized with this [Jira Task](https://mozilla-hub.atlassian.net/browse/FP-140)