Battery percentage increases after cold boot iPhone 7 - okay in Smart battery case.

iPhone 7 approximately two years old running iOS 12.3.1

Always in an Apple Smart Battery case since new.

When case runs out I sometimes use it on the phone battery (outside of the case).

Out of the case the level drops (quite quickly) to around 10% I turn the phone off and back on and the battery level shows 45-50% !

The Battery preference says Maximum Capacity 91% Performance Management has been applied.

So why does the level revert to a higher percentage after a cold boot and is there an app which tells me which apps are using the most battery “right now”?

Is there anything which will tell me how many charge cycles the phone and the battery case have had?

Many thanks

Mike