Cool score is the newest addition of bonus points and it's added at the end of each act based
on your performance.

But what affects the amount of points that you'll get?

At the beginning of each stage your cool score is already at 10000 points. Yep, that's right! Every act
assumes perfect cool score. That score, however, gets reduced every time you get hit.

I haven't tested whether losing a life reduces it more than say losing just your rings are yet to be tested. However, I've tested the following:

1) Using the restart option from the pause menu: Restarting the act this way carries your cool score over. Say you got hit once and you decided to restart the stage. Your cool score now is assumed to be 9000 no matter whether you'll get hit during this run or not.

2) Restart a world through the save select menu: Restarting this way is obviously worse since if you were in act 2 of any world you're stuck on going back to act 1. However, this is the only method to reset your cool score back to 10k.

3) Dying always drops your cool score to 0 (thanks @Boa Hancock).

Nope.

As long as you can sacrifice lives to farm score over and over, and as long
as you can just restart any act carrying your score over and over again, score implementation in Sonic games has a long way to go (or even don't go anywhere and get scrapped entirely).

With that said you can still feel good for hitting that sweet 10k at the end of every act because there's a difference between the player who gets hit a dozen times and the player who flawlessly breezes through every level.

In other words, the scoring system of Sonic Mania is a step towards the right direction of measuring performance but not quite there. Another genre that still uses scoring for this use is shmups but for shmups you rarely have to start over the stage, and using a continue resets your score back to zero. There's rarely a "scummy" method of accumulating a high score. For a more polished games that are score oriented there's still "shmups" like Mushihimesama, DoDonpachi resurrection and Crimzon Clover (all on Steam).

I hope that I helped you understand what cool score is.

This isn't really part of the guide but an opinion piece I decided to add because, unlike people who only see problems, I also want to think that I see solutions or at least one out of many possible solutions.

The idea of score tracking is older than everyone here, since sports and board games are as old as society. Tracking score is a measurement of progress in games that have a clear start and finish, but when you introduce it in single player games you do this so that people can compare their performance before and after. But they also want to compare their performance with friends. Leaderboards are meant to be that representation.

Now, at the time I'm writing this edit, the game is structured in a way that leaderboards make no sense. Because score makes no sense. I mean, okay, I see numbers growing, I feel good about me accumulating more of them but what do they mean?

For score to be meaningful it has to represent your performance. "Cool Score" is a great idea because it rewards you for going through a stage without getting hit. Whitehead went as far as making it hard to be "reset" for that.

But when the game hands you over lives like candies, people will find ways to milk them. The game ends up rewarding people who find loops to "game the system", which is done easier when the screen doesn't scroll automatically (like in the case of shmups).

The solution for that is to introduce a separate scoring mode, which is "one life only", turn the 1-up monitors to award 10 rings, and then make sure there's no glitch-y way of hitting 999999 like in the case of Super Mario Bros 1.

After trying to contact people around Sonic communities to ask them how interested they would be in scoring runs, nobody was really happy about it. What I'm saying is, I'm actually surprised this guide is popular enough as it is because my impression was that, nobody cares about scoring when achievements are a thing, which cap at 100% and result in a binary black&white "you either have the trophy or you don't" comparisons which I find lacking in descriptiveness when it comes to separate the good player from the great, but that's another topic.

Anyways, thank you for reading my rant and my guide (in no specific order).