Hi Matt
Hard to see the details on the photos but the battery could well be the cause, although it looks like you now have several of the computer modules sulking and not talking to each other. This can happen if the battery voltage gets low and corrupts the software. My sportbrake had problems in lockdown when I left it for a month, battery went flat, jump started OK, but rear doors and windows were now permenantly locked 😞
I think the car "stores" 3 copies of the entire software in various modules and it is possible (if you know what you are doing and have the correct diagnostics) to repair the corrupted software with a "clean" copy.
Apparently there is a place in Milton Keynes called E & E who are really good at clearing the codes and sorting the module issues. Obviously a long way from you, but might be worth a call. Otherwise I suggest a specialist with the Autologic diagnostics as they seem to get the best results. From previous threads on here if you go to Jaguar they just advise changing each "faulty" module with a VERY large invoice at the end.
Good luck
John