Against The Tsardom of Russia Level 2: a damaged Explorer with a Health bonus ends the turn in a way where it won't heal (e.g., in Shroud of Silent Mists' lands). It should be destroyed when the health bonus wears off – is it saved?

Against The Tsardom of Russia Level 2: a damaged Explorer with a Health bonus ends the turn in a way where it won't heal (e.g., in Shroud of Silent Mists' lands). It should be destroyed when the health bonus wears off – is it saved?

No. It's not in the context of an action, so "A Sense for Impending Disaster" doesn't save the Explorer.
(This is a provisional answer – if further cases like this suggest that "Effects expire" needs to be an action, it could conceivably change, but that seems the less likely case.)