My iPhone's battery rose without charging

Unless when you tap on Battery Health and it is below 80%, I don't see anything bad on your screenshots or description.

Only thing I don't like is that you seem to have shut down the phone for charging. It cannot use Optimised Charging if you do that, and battery life may be affected.

The recommended method if to keep it on all the time, charge all night, every night, and never run it flat.

Once optimised chargimg is set up you will see (after a few days) this pattern. where the last 20% is applied late in the night.

If battery "Health" (actually capacity) is below 80% have apple fit a new one for about $69.

Don't turn it off unless there is a problem. Then you will not need to turn it on and be surprised that the battery has revovered from a thrashing on a game.

Battery health and battery charge levels are both approximations.

In terms of the available charge level increasing slightly after heavy use, that is not unusual. Battery level is an estimate based on parameters like current draw. That estimate will dip during heavy use, but once that heavy use stops and the device is idle, the estimate will change now that the heavy current draw has stopped.

Nothing about the battery charge level, capacity or health can be measured directly. They are all estimates computed from algorithms using indirect measurements. They inherently fluctuate somewhat over time and dependent on usage pattern.

Chill, no problem.

Take my advice on correct charging method.