Polar bears, I feel are quite a neglected mob, outshined by mobs like the arctic fox, dolphin or panda (which are amazing mobs).
Here’s how better behaviour in my opinion could work:
Polar bears should have a territory assigned to them, the territory size depending on the dominance level of the polar bear, there would be three dominance levels, in order for the player to recognise how dominant a bear is/how strong the following behaviour would be, polar bears could come in three sizes, 3 blocks, 2.5 blocks and 2 blocks long. Polar bears would have the ability to detect the levels of other polar bears and act differently depending on what type of bear they are.
Polar bears with cubs, their dominance level will usually range between 2-3, they will behave pretty much like how they do now except they will also be aggressive to almost any mobs that have wandered into their territory. Lower level polar bears will usually scarper once they detect a protective polar bear, however higher level polar bears may engage in a dominance roar off, upon which the bears may stand on their back legs and wiggle their arms and roar. If a parent protective polar bear loses a roar off, it may lose its territory.
Bears with curious behaviour would wander around freely with no fixed territory, curious bears would interact with redstone buttons/levers, follow players until they are bored/enter a territory of a bear with a higher dominance level (upon which they’ll scarper) or if a firework is released (scary noise). These bears would rarely engage in a roar off with a bear with a higher dominance rating.
They would be hostile to any player with a fish/fish bucket in their inventory or hotbar that has wandered into their territory. Once they have detected the player they would pursue you then steal your fish/fish in a bucket.. Once they’ve got your fish they will then proceed to run or swim away with it in their mouths. You can counter these thefts by having a puffer fish in your hotbar (yuck). Hungry polar bears will wander into another bears territory, no matter what the dominance level, if it comes across the other polar bear they may engage in a roar off, the winner receiving a higher dominance level and the territory, the loser losing a dominance level and their territory (bears without a territory would then become a curious bear).
Some Polar bears would be attracted to villages in what they consider to be their territory. Bears like these could scare villagers that live in snowy biomes into or away from their homes. To counter this you could build a snow golem in the village to frighten them off with snowballs, fireworks would also work as a counter. This would provide a good use for snow golems, more snow golems may be needed depending on the urban bears dominance rating. Urban polar bears will rear up and tap on glass and doors, they will also sniff around barrels near fishermen huts.