[TST-E5] Live tests get one server lifetime and one per-test cleanup scope #494

Part of #350, the quality-refactoring roadmap (road to 1.0, step 3).

Goal: Live tests get one server lifetime and one per-test cleanup scope.

Lane: Tests. Status: todo.

Every PR of this epic starts its title with [TST-E5]. The finding issues it closes are linked as sub-issues; this issue closes when the epic's last PR merges and master CI is green.