Pipe `Duration`-based time information through scoring pipeline

Pipe `Duration`-based time information through scoring pipeline

In the coming commits, the `T: Time` bound on `ProbabilisticScorer`
will be removed. In order to enable that, we need to pass the
current time (as a `Duration` since the unix epoch) through the
score updating pipeline, allowing us to keep the
`*last_updated_time` fields up-to-date as we go.