It looks like two factors are at play. The screen time issue is a software bug and it just needs to be ignored until the next update. The background activity is due to the recent update and should level out in a day or two. After an update, a lot of activity goes on behind the scenes (background activity) and it is now normal for extra background activity for three to five days after an update if you’re iPhone is using AI.
In the meantime do a forced restart of the device, just make sure it’s not a particular app just being stuck in a loop. A forced restart does more than just turning your iPhone off and back on. Please review the instructions if you’re not familiar with the procedure. When you get to the part where you are holding the side button (power button) for 10 seconds waiting for the Apple logo, don’t worry if it takes longer. Please hold the side button until the logo appears, which can be 30 seconds or longer.
Force restart iPhone - Apple Support