Not sure if it’s still legal but 20 years ago when I was a waiter we would marry the ketchup bottles every night. Due to this I generally don’t use ketchup at cheap restaurants (and especially will not use the bottom of a bottle as who knows how old it could be).
Fridge for me. I buy the 1QT+ size of Kikkoman once a year or so.
I have some old Chinese style dark soy sauce in the fridge that I should probably toss, but it still does the job. There is also some Filipino soy sauce for chicken adobo in there and a Tamari that I tried once and didn’t like.
Highly acidic foods are fine at room temperature. So is very salty stuff. Ketchup is acidic enough to be safe. Soy sauce is borderline on acid but very salty. This is based on a thorough Internet search of like 5 minutes so you can totally bet your life on it.
no fridge, but we go through it fast. Likewise, hot sauce, sriracha, sambal oelek all stay out (but we go through those fast too). I cook a LOT of Asian food…
I usually put the ketchup in the fridge, but honestly, that’s more because I think it tastes better cold. Having worked in restaurants, I know it’s safe to leave out.
For eggs, I tend to go with inertia. If they’re not refrigerated when you buy them (like from the farmers market/egg farm) then they stay out, and vice versa.
American eggs have to be refrigerated because they’re washed (eggs you buy directly from the farmer are (probably) not washed). Once they’re washed, it’s easier for… bacteria to grow on the shell? IDK the specifics, but that’s the difference.