How to repair a burnt PCB?
The first thing I would do is give the PCB a good clean, to try and remove as much of the carbonised buildup as possible.

Then I would start testing, if parts of the PCB have become conductive it may be necessary to cut slots or re-route signals using wires to fix that.

The good news is it seems your PCB already has a bunch of slots in it and the damage looks mostly superficial to me. I think there is a good chance after cleaning that the PCB itself will be fine.