How do I revive downed party members?

As it turns out, Inns are the way to rest and restore your HP - in my case, it was simply a matter of still being in the prologue, and the option not yet being available. When I went back later, "Rest" was available as a conversation topic.

Dead on your feet? Sleep at an Inn!

For future players also struggling with the no-inns-in-prologue...the sewers are still accessible (south of the church) and the orbment charging station is close to the entrance!