Like everything related to background stuff won't get any borders at all. And keep everything that you can collide with with black borders.
It's definitely a way worth following.
Graphics is good and the animation of cats allows to believe that the dinosaur's animation also will be great
I think you should make the size of the dinosaur smaller as said above and instead of making jump height less I would consider adjusting gravity first and then make double jump a little bit lower.
It's not clear that you can destroy cats by jumping on them. I discovered this opportunity by accident when I was in this part of holes and cats running the same direction as dinosaur.
Maybe you should try to design some obstacles where it would be necessary and obvious to use speed up button because at this moment it seems needless. You've chosen quite difficult way of gameplay design. Usually in this type of game you have one button for jump/double jump and the second one for attack or slide down under some obstacle - such design makes it easier to achieve more challenging and diversified entertainment. But not everyone has to make it in this way and maybe you'll achieve good level of fun and engagement with your desing. Good luck!