Add browser.engagement.inactive_period_duration, a labeled timing
distribution that records the duration of each period the user was
considered inactive, measured from when the user goes inactive until
activity resumes. Combined with consecutive_active_ticks (Bug 2050093),
this helps reason about user interaction patterns more holistically and
informs whether additional active-tick intervals should be introduced.
Like consecutive_active_ticks, the metric is labeled to track both
streams side-by-side: the 'active_ticks' label uses the legacy
user-interaction notifications (all events), and
'active_ticks_non_synthesized' uses the corrected variants from
Bug 2050081 (excluding synthesized mouse and pointer events).
An inactive period in progress when a ping is submitted is recorded in a
later ping once activity resumes; a period active at shutdown is dropped.
Differential Revision: https://phabricator.services.mozilla.com/D311382