Hello! Super Noob here!

I am going away for a long time so I wanted to clean up the corrosion off my battery for long term storage and possibly disconnect it.
Following a youtube video, I threw on some hot water, thinking that would be enough to remove the buildup, but I then added some baking soda to help. Then I added a gel around the copper points so it doesn't get the battery building faster in the future.

My mistake was that I didn't dry the connections before attempting to disconnect the battery. The headlights flashed a few times, and when I tried to restart it, the odometer went crazy, it attempted to light up, but it couldn't start. The power steering and even brakes are stiff. So I took the cap off the nubbin next to the gear shift and pushed it in to release it so I can manually shift it in neutral. Parked it, and left for Texas. Of course I did this right before I leave for my trip.

Is there something I can do to reset the whole system in order to start? Or should I not do further damage and send it to a mechanic? Is this one of those really bad mess ups that I need to take it to the dealer? Do you think this might be covered in my extended warranty?

Any and all support would be greatly appreciated. How bad did I mess up?
FYI, I have a Mazda 3 2015.