This is the worst kind of fault to have on a car :0(
My approach would be to work through it logically. What is t he history? What has happened to the car in the past that might have resulted in damaged wiring, plugs or components? Aftermarket accessories fitted? Dashcam, lights, cheapo gizmos? Impact damage? Water damage? Is the new battery the correct one for the car? Was it correctly coded to the car?
The odds are that some event in the past has caused this fault. It could be a random chafed cable but it's not very likely. Where did you get the new battery?
Ok so I've had the car since September last year, I'm the second owner from new. It's had its moments, in November last year I lost all power that was a oil pressure sensor, new battery fitted in February (unsure how to know if this was coded or not but it comes up with multiple warnings afterwards and after turning the steering wheel a few times and driving it the lights went out) most long journeys it pings to say low tyre pressure which normally it isn't the cases. It's been well looked after serviced etc. Dash cam was fitted last September and other than that nothing has been touched in the car.
There's no fixed pattern to the car doing this, sometimes it's cold, sometimes after a couple of short journeys, sometimes after a longer journey so I can't pinpoint a specific time it's doing it.