It looks worse on the picture than in real life because of the flash. When I saw my pic, I considered Photoshoping it before posting, that's how ashamed of myself I was...
There was a lot of that white/yellow foam on the terminal, but not around. Then I had to remove the terminal to reset the whole unlock/no start issue, that's when all the residue spilled. I guess it then absorbed the humidity and that's how it looks now.

I guess cleaning the terminal and cable won't be enough and everyone here will tell me to buy a new battery (this one is from mid 2016 according to the label, and supposedly has a 6 years life).