When a live-priority plugin (e.g. live sports, flights overhead) preempted
the rotation, the controller overwrote current_mode_index with the live
plugin's index. Once live priority ended, rotation continued from after the
live plugin's mode, skipping every mode between the interrupted position and
the live plugin. With a live plugin late in the order, modes just before it
were starved indefinitely.
Save the rotation position on the initial live-priority switch and restore it
when live priority ends, in a new _apply_live_priority() helper. Add
regression tests covering resume, no-double-save during the hold, and the
idle no-op.
Co-authored-by: Claude Opus 4.8 <noreply@anthropic.com>