[Bug]: Qualifying Q-part badge switches late

[Nicxe]

Related to #50, but tracked separately to avoid mixing different symptoms in the same thread.

During qualifying / sprint qualifying, the Q-part badge appears to switch to Q2 or Q3 only when the first driver completes a lap in that segment, instead of when the segment itself starts.

Expected behavior: the card should show the active Q-part as soon as the new segment starts.

Actual behavior: the badge seems to lag behind the actual session phase.

Please use issue #50 only for the driver-order / inherited-rank problem. This issue is only for late Q-part badge updates.

[Nicxe]

I’ve now fixed this on the integration side.

The root cause was that the qualifying card already supported showing the active Q-part immediately, but the driver_positions sensor could still lag behind when TimingData had not yet exposed the new segment at Q2 or Q3 start. The integration now falls back to the qualifying part tracked by the session status flow, so current_qualifying_part updates as soon as the new segment begins instead of waiting for the first completed lap.

This means the fix is an integration update, not a card configuration change. I also added regression coverage for normal qualifying, sprint qualifying / shootout, and the case where the Q-part changes without a new driver timing update.