Ipad pro 12,9” first gen battery problem or update related?

I have an iPad Pro 12,9” first gen. It is a replacement that I got in 2019 (the first one got replaced because it didn’t recognize the SIM, the second died after 3 months).

It is well used. About 5 to 6 hours a day. So, yes more than 1.000 batterycycles.

Before the update of iPadOS to 16, no battery related problems occurred.

After the update to iPadOS 16 the iPad crashes as soon as I open an app that starts to refresh its content at opening. Even with a fully loaded battery. When I restart I get the batteryindicator with the red indicator and the cord, indicating a low battery (it’s just diconnected after a 100% charge).

This does not happen as long as the charger is connected and charging.

So there is clearly a sign that the iPad is using to much energy from the battery.

The big question however is: is this caused by iOS16 or by a bad battery?

will a new battery solve my problems?