Nice looking game !
I just want to report that sadly I couldn't go very far due to a bug... The yellow lines do not work !
When I go forward and jump on them, I cannot "grab" them, even if the hand icon flashes quickly.
There is a screenshot : 
I am using Windows 10 64bits with an AZERTY keyboard for which I switched the layout to QWERTY using the ALT+SHIFT Windows shortcut
Sorry to hear that you are stuck - if you can JUMP and MOVE, theoretically, you can climb - press W and JUMP at the same time towards the yellow ledge, and then hold SPACEBAR to climb. I suppose you didn't hold it when you were trying to climb?
Anyway, thanks for reporting! I don't know much about AZERTY keyboard though, let's hope it has nothing to do with hardware XD
So sad... If you still want to experience it, I would recommend you press H to unlock all abilities so that you can double jump that ledge, and also it grants you dash by pressing Z.
Actually the music is taken from Octopath Traveler, if you are interested in JRPGs, give it a try! (fun fact: as a pixelated "2D" JRPG, it was made by UE4)