Starting from 27th March 2021, a great reorganization of the leaderboards has taken action. The main purpose of it was to make Happy Jump's leaderboards to have more speedrun-related elements, because before there were not any of them. Second thing was to double check every verified run due to a little bit too chaotic and unclear method that had been used in the past.
Thanks to @ReniReni, several new speedrunning categories were created. They are called as "Points" and "Death". The former has also five speedrunning subcategories (1,000; 5,000; 10,000; 20,000; 50,000 points).
High Score leaderboard has been reformed as well. All previously verified runs (I mean, those that were verified before 26th march 2021, including this day) from the old "High Score" leaderboard dedicated to Happy Jump, and "Ice Cream Jump" dedicated to its clone, have been double-checked. I have noticed that many runs no longer have any source availble to be a proof showing clearly the time that was reached by a speedrunners, however as long as they are not deleted as runs, they are going to stay on the leaderboard, since they were once verified in the past.
Speaking of clones, a separate Misc. category was created for the highscore runs of two clones of Happy Jump, which are: Ice Cream Jump and Happy Poo Jump.
If you have any other suggestions, opinions or objections regarding the recent huge reorganization of Happy Jump's leaderboard, feel free to write them below this post or just by contacting one of the moderators.