It is a very nice game. Definitely to learn from.
In terms of improving I haven't really made a platformer but I think these should help. Please remember this is my interpretation and could be wrong.
1.) I think your using a capsule collider 2d on the character what does lead to the character sliding off the edge of tiles. Can either change the collider or use some kind of edge detection and mix with tip 2.
2.) Coyote time. Just that little something as you get to the edge but don't quite make the jump in time.
3.) Personally I would slow down the animation on the fruit. Just feels faster it runs faster than the rest of the level.
4.) In terms of jumping . Take your second screenshot for example. Your jump is great to jump through it (I guess the intended route), but is a bit too vertical to say jump over the blade underneath. perhaps add some forward movement/momentum.
5.) In terms of level design. Use that second screenshot again. If we took them boxes away and just used the rectangle platforms, it would probably feel neater and allow space to use tip 4s improved jump. I understand it may be intended to wall jump here. a mechanic you have implemented well.
Hope that helps. If want anymore be sure to reply or message. Can't wait to see where the project goes.