It SHOULD work that way even on webgl. do you know which checkpoint you quit on? maybe it’s a bug with that specific checkpoint
sorry for the very late response , i quit in the first level at the zig zag wall section that then jumps over water , the water should have 2 rombus like structures to the left and the right , you jump right inside the castle and on the floor there should be a red carpet , here is some additional information that may help , the data was lost when i refreshed the browser , also the browser i am using is brave , when i try to play all three save slots say new game , It also may just be an issue on my side , is there some sort of manual save/export ? if yes i might have missed that which would make sense . if you need any more info feel free to ask , even though i might respond a bit late again ,