This is gonna be a bit of a deep critique review for you.
The idea is fun and the aesthetic definitely knows what it's trying to be and has a lot of potential.
The camera feels a bit low as if the player is perfectly centered in the camera which at times feels off.
There's no way to see your score while playing or even see highscores right now anytime after. So the only time and the last time I see a score is on the death screen. Which makes me want to play less because that mentality of "I'll beat my score this time!" just doesn't exist. And seeing a score while playing is super important. If I can't see my score I'm really not given a reminder of what I'm trying to accomplish or how close I am to it. Seeing a score and highscore often makes the gameplay a bit more intense. Being a few points below your highest score is always nervewracking and fun.
The parallax background sometimes makes the platforms look jittery which can be a little jarring. I can also at times jump above the background which is definitely strange looking.
The collision boxes sometimes have the player a little in the air which looks off.
The platforming feels a little floaty and really tuned for the game; which makes things feel strange sometimes personally.
Adding keyboard/controller interface controls also would be a nice touch so I don't have to reach over to my mouse to start the game and restart it.
There's potential for the game but it definitely could benefit from some work.