Recently some brown bears appeared in my region.
Should we encounter one, is it a good idea if we opened a jar of honey for the bear so we would have time to leave?
No, not a good idea at all. The bear is now used to people and food together and will seek people. This will not end well for the bear and may very not end well for the next people it encounters.
"when your life is in danger"
Respectfully, your life is not in danger and feeding bears can put other people's lives in danger later. If your life really was in danger because you are an active target of attack - say you were too near to some bear cubs - the bear would most likely not pay any attention to the honey and would attack you. Consider also that carrying food around in bear country is likely to attract them.
The general idea with a bear is to back away slowly, possibly speaking to it, and not look it in the eyes.
This video is for North American bears.
From looking this up a bit, 1, 2 3 seems like you are indeed dealing with brown bears, i.e. pretty much a what we would call a grizzly, not black bears (a relatively easy way to tell is that big hump on the back, right behind the neck). If it was an actual North American grizzly this would mean:
Bears are however not sharks and certainly not crocodiles. They are smart enough to avoid humans under nearly all conditions (unless they associate people with food, which is why the honey idea is bad in practice) and have very limited interest in you as something to eat. Be cautious but appreciate the possibility of their presence: they're a bit of wild nature that could hurt you but you are much more likely to be be hit by a car while walking. An encounter is a good story to have folk buy you a beer once COVID is gone ;-) I've seen 4 or 5 myself on foot/bicycle, not counting ones I've seen from a car.
If you are truly concerned, and if you have access to it, buy some bear spray. It's about $20-30 where I live (Canada) and lasts 3-4 years. Note that, at least in Canada, there are tons of regulations about transporting it (don't bring it in a plane).
p.s. One last thing, which is counter-intuitive. Leave the dog at home, or leash it, unless it's trained for bears. A not uncommon occurrence goes like this: dog finds bear, barks at it, bear charges, dog runs back to master with bear in pursuit.
Some extra reading. Good, but they tend to mix blacks and grizzlies together in the grizzly coverage.
When the bear is actually dangerous is when it is angry or frightened, and if it is angry or frightened it won't care about your silly jar of honey. Dare I say you're thinking too much like a city person? Your mindset is completely wrong. This is not like a clingy housepet that you're trying to distract for just long enough so you can leave the house.
Imagine if the roles were reversed. If you a bear suddenly startled you and it dropped a bag of money in front of you so it could get away, would you care about the bag of money at all?
There are some other good posts, but one thing I haven't seen brought up is that bears are thought to have the best sense of smell in the animal kingdom, possibly 7 times as good as a blood hound, 2100 times as good as a human.
So carrying that jar of honey around with you might just entice a bear to follow your trail and get at the honey. Just sayin'...