I appreciate you must like your chess game but it is using quite a chunk of battery.
So is Google Chrome which I believe is a resource hog so personally I've disabled that and use Samsung Internet.
Have you considered clearing the phone's system cache files @YannJollien which might help.
Clear your System File Cache via the instructions in the Samsung Link. You may need to hook upto a computer or insert your headphones to get to the recovery menu. https://www.samsung.com/uk/support/mobile-devices/how-do-i-clear-the-cache-on-my-device/
Also looking at your screenshot your signal bars are pretty low which will mean the phone is working harder to maintain connection, and voLTE will be using more resources too.
Android 12 with Samsung One Ui 4 is a large update so it may take a short period of time for the phone to settle and apps optimise.
Daily Driver > Samsung Galaxy s²² Ultra 256Gb.
Samsung Gear s³ Frontier Watch.
Samsung Galaxy Watch⁴ Classic.
The advice I offer is my own and does not represent Samsung’s position.
I have no affiliation with Samsung.