Okay, no. These are literally contradicted facts. In JJ1, Jazz is described as a soldier of fortune, and the first thing we see him doing is planning to bring a cat to a planet of rat creatures, essentially planned genocide in recompense for them stiffing him on the bill. He hangs out in a bar and gets drunk. Later on, in the animated cutscenes, he takes on a more classical cartoon feeling, playing fast and loose with real world physics, but at no point does he act like a furry. Furthermore Eva is in no way his lover because the two of them have never met.
In Jazz3D, Jazz's gun is objectively smaller than him. It's true that he can shoot anything he wants to, perhaps more than ever before considering he can attack other rabbits, but there is a specific plot involving rescuing his children and a third dimension. Mayhem is never unprovoked.
In terms of stylistic evolution, Jazz 2 was a significant break from JJ1. If there had been a community at the time in the sense that there was in 2000, people would have been upset. Jazz3D took significantly fewer chances with character and design, and suffered comparatively little complaint on that ground, while JJA went all out and as such incurred great wrath.