Did I Brick my Controllino?
It certainly looks like the INT pin of the RTC can kill the whole unit. Bit of a FUBAR on their part I would say. 


  Is it a viable idea to try and burn a new bootloader ?


If the problem is that INT pin then you won't be able to replace the bootloader, and even if you did it wouldn't fix the problem.


  Is there a simpler way to reset the state of the device?


It looks like you will have to make a hardware modification - cut the connection between /INT and /RESET on the board - if you can identify which track that might be - or use a soldering iron to heat and lift the /INT pin of the RTC chip, which might be easier, depending on what the chip is (they are amazingly short on information).


  What did I even do wrong ?


Probably nothing serious - it's the design that is at fault. Anything that has the potential to completely cripple a system like that without even trying is just idiotic.