Revisit `onActive` and `onInactive`

We should revisit the `onActive` and `onInactive` handlers at some point to come up with a better signal for the client being inactive.

Currently it is flagged as inactive as soon as the extension window is closed, but users may close it to view a dapp, opening it seconds/minutes later.

We may also choose to implement new handlers for this case.

Blocked for now.

Start by tracing the existing `onActive` and `onInactive` handlers and how closing the extension window currently marks the client inactive. Determine whether improved signaling or new handlers can distinguish closing the window to view a dapp from genuine inactivity; the issue is done when that behavior is resolved and the chosen handler approach is implemented.

Written by the indexing model from the issue text.