There is a pathogen, Bacillus cereus, which can grow on rice left out at room temperature and cause food born illness.
I was unable to find any references to proper fermentation of horchata which is normally not fermented as far as I can tell.
You may wish to be cautious in the future.
Edit: See my question here. I plan to update this answer after I get an answer to that question.
I'm a beginner when it comes to this (I've fermented a few quarts of pickles with Fermilids), but from everything I've read, you'll probably survive if you eat it. However, if you add too much salt, that can kill the bacteria needed to do lacto-fermentation, and you may end up salt-curing your vegetables instead of fermenting them.
From what I understand, a 6% salt brine solution is about 3.34 tablespoons per quart of pickles. I've read that your brine should only ever be between 1 to 3 tablespoons of salt per quart of pickles (if you're not using a starter, and you can perhaps use less salt if you use a starter), and that you should use more salt the warmer it is (but not more than 3 tablespoons).
I believe the delay is partially, if not entirely, due to the salt. I imagine that the activity is from beneficial bacteria that needed a longer time to get started, due to the salt. I don't know of any bad stuff that would survive those conditions, if you're not getting mold. I can't give you a definitive answer here, but from everything I've read, that's my opinion.
I used 2.5 to 3 tablespoons of pickling salt on a quart of rhubarb, and I didn't taste much lactic acid in it after three weeks. However, with about 2 tablespoons of pickling salt, and a probiotic (a chewable L. acidophilus and B. lactis tablet) my rhubarb tasted pickled after 6 days. Temperatures for both sets of pickles were between 69 to 73° F., I believe.
From those results and the results with my radishes, I personally would be leery about using more than 2 tablespoons of pickling salt for some vegetables. I'm not sure about cabbage, onions, oranges, etc.
Remember, though: I'm new to this. So, you probably know things I don't.
You'd think onions would ferment quickly, because they're known for their content of FOS (a pre-biotic and sweetener). However, from my experience, I know oranges can take a really long time to compost in a garbage can with a lid on it (they're still whole and visibly oranges after a couple years). So, maybe the orange juice contributed. I'm not sure how LABs respond to citric acid.
Best Answer
It sounds like it's fermented, and more harmful bacteria or mold could definitely have grown without being visible.
So it's not safe, in that there's definitely some risk. It's hard to evaluate exactly how risky it is. It sounds like you're already routinely taking risks by eating iffy food that's not obviously rotten or moldy, so you certainly could choose to take that risk here. I'd really advise against it, though.
Remember, food poisoning isn't just about stomachaches. If you end up in the hospital, it's going to cost you a lot more than a replacement jar of applesauce.
As a side note, applesauce generally requires refrigeration. The jar you have almost certainly says "refrigerate after opening." So it may not be a good choice for an egg substitute. You might want to look into actually shelf-stable substitutes. If applesauce is working for you, flax (or chia) or mashed banana might be good options. Flax and chia are totally shelf-stable, and while bananas don't last forever you can at least buy them as you need them.