‘Use By’ means open and consume that product before that day, for safety.
‘Best Before’ means it may not be unsafe after that date, but it will be past its best and not taste great anymore.
Those dates refer to the product when it is fully sealed and stored as recommended, because packs are usually manufactured in a way that all the air is removed and there’s either a vacuum or a sterile gas mix as the ‘air’ inside a pack. This helps stop the food from going bad quickly.
Once a packet is open and the outside world can get in, two things are a problem: oxygen and biological contaminants like dust/bacteria/fungi (these can be things that make you sick, but usually they are things that just spoil the food). Oxygen can start causing fats to go rancid and taste bad, and it also lets any microbes start growing.
Two things, -it’s a pasteurised product, therefore it does have microorganisms (pasteurisation doesn’t kill all bacteria) that can spoil the product-Due to its high moisture content, it’s particularly susceptible to microorganisms. In food science there is this concept of water activity (aw) it ranges from 0 to 1… The higher the more susceptible to microorganism growth… Mozzarella aw should be around 0.9+.