I usually lacto-ferment hot peppers for 1-2 weeks and eat them uncooked for the probiotics. Haven't made hot sauce yet, but now I know I have to ferment for months. I'd put the brine back in the peppers after cooking to keep it probiotic. Had an idea for jalapeno + poblano + kiwi fruit hot sauce where I roast half of the peppers before fermentation.
Kept some "raw", but generally cook it for shelf stability if putting up a good sized batch. I've got kraut and kimchi in the basement frig, and Mrs. Duck ferments onions, carrots and a tasty curried cauliflower - and our daughter in/out-law brought us a couple pints of homebrew kombucha last night. Pretty sure we're chock full of probiotics!