Critical notifications on apple sports iPhone app.

If I understood the problem correctly, the issue is caused by Live Activities, which update scores on your lock screen and can bypass Focus modes, causing vibrations and spoilers.

Open iPhone Settings, scroll down and select App/Sports, tap Live Activities, turn off Allow Live Activities.

This will stop the app from sending flash updates, saving both your sleep and your TV viewing experience.

You have no control over the timing of notifications. They will arrive when arrive.

However, you have multiple options to control haptic notifications on your iPhone...

1) You can suppress Haptics (i.e. vibration) when your iPad is set to its silent mode:

Settings > Sounds & Haptics > [Ringtone & Alerts] Haptics - change from Always Play to Don't Play in Silent Mode

With this mode selected, ensure that you either manually set your iPhone to silent mode at bedtime, or configure the Do Not Disturb focus mode for your quiet hours.

2) Turn-off System Haptics. This will completely disable the vibration feature for alerts:

Settings > Sounds & Haptics > System Haptics - set to OFF

3) Disable notifications for the Apple Sports App:

Settings > Notifications > [Notification Style] Apple Sports > Allow Notifications - set to OFF

The pic below is self-explanatory.