HP=moral+collateral damage, which would make it somewhat of a Hitman style strategy game to get done what you need to within the bounds of what Superman is... A giant moral pussy.

So while you can melt someone from space or fly through the building instead of around it, you cannot if you don't want him to die of sadness, and managing that when you easily can, is likely hard.

You could take a look at Megaton Rainfall. Not Superman specifically and in 1st person, but a total power trip for sure.

Yes. Give me the opposite of a soulslike.

There is an upcoming game called Undefeated Genesis. However, it is an indie game, so temper the expectation.

I would also take a bizarre, reverse tower defense game, where you have increasingly large hordes of bad guys at your disposal trying to take down an ever more powerful single Superman.

Superman 64 should've been this. Like GTA, but with with opposite goals. They had the Timmverse look. They had mechanics for tossing cars and punching robots. They just used them in the worst possible way, because of absurd corporate demands.

The clever workaround for players being dicks is to say Bizarro's on Earth, and obviously thinks he's Superman. So any time you go completely over the line or fuck around beyond excuse, you get a soft game-over where you catch your reflection and it's not Kal-El.

What I'd pitch is a fairly short game with replay value in optimization. It's a day in the life. Superman has the ability to solve every problem in the city, that day. Superman has the ability to solve several major natural disasters happening around the globe... and still solve every problem in the city, that day. You, the player, are going to jump through your ass trying to schedule or predict more than about half. It has to be fair. There has to be a way, on every single playthrough, without memorization or guesswork. But it can be obscenely hard. It can be controller-through-television levels of difficult, both intellectually and mechanically, because that's in-theme. It underlines how good the man himself must be, in order to stop every mugging in Metropolis, instead of just the ones he comes across. And it lets you feel his frustration when even one slips through the cracks.

Anyway, escalate through a few specific "heavy" days, spread across a month or so. At first you're handling petty crime across town, with an invitation to rescue people from rooftops when a dam bursts in another state. By the end you're fighting Brainiac atop the Daily Planet, and while he limps away from having all three of his dicks twisted, you find a quiet moment to help a child climb out of a tree. High-level play involves hearing about a disaster before it happens, so you can stop the dam bursting in the first place. Or throw a tornado back into the clouds, or redirect the faultline from an earthquake, or whatever the problem is on this playthrough. It's variable enough that you can't just fly somewhere pre-emptively (most times) but frank enough that you might prevent it the first time.

Knowing what's right to do isn't easy, but it's simple. Knowing how to do all of it at once is neither.