It being textbook standard 敬語 really cements that.

Only just noticed your username, Christophe.

I've fought mud crabs more fearsome than you.

cough

よくできました

Maybe they are in a big cat sanctuary

It's mistranslated. They say hyō which is leopard. Puma is pyuuma.

So the leopard could be in Africa or the tiger and leopard could be together in India. Still wrong but slightly less so.

That’s why the one guy thinks the other is lying.

um - - it's a video game called Africa? maybe. Nintendo is completely out of ideas. They're lazily flipping through pages of Encyclopedia Britannica and stuffing content into a game. The result isn't great but it's standard fare for them

profile pic checks out

Or a puma for that matter. Or maybe they're just visiting a zoo.

Although うそ literally means "it's a lie", it should have been translated to "Really?"

It’s polite in the grammar sense. Japanese has different verb endings depending on the level of politeness. Speaker A is using polite form while B uses casual form. This is normal when the speakers are not on the same social/hierarchical level. Like a conversation between an employee and a boss, or a young person and an older person.

Also A is using polite sentence endings. 〜ます, 〜ました, and です.