I want my Mac Studio to power on when the AC is on automatically

It might not be exactly what you want, but you can configure a Mac to turn on automatically after a power failure: Refer to Start up automatically after a power failure in Change Energy Saver settings on a Mac desktop computer - Apple Support.

We have to interpret that Apple Support document literally: If you intentionally shut down a Mac, and then remove its power source, it will not automatically start up when that power source is restored. On the other hand an unexpected loss of power causes a different shutdown event to be logged; an entry noted by the Mac when power is eventually restored. That unexpected loss of power must have occurred for it to subsequently start up automatically.

Perhaps that will help, because a Mac that has been properly shut down will remain shut down — unless it has been programmed to start up at particular times as noted by my colleague PRP_53.

Another reason NOT to do that is that a Mac has an Always-On internal power supply. This generates very small amounts of power to backup the clock chip and the parameter RAM.

Without external AC power available it will rely on the internal PRAM backup battery to maintain the parameters that make staring it up and using it on a whim easy. You will wear this battery out sooner than necessary.

A Mac Studio is a Desktop Computer - right ?

It does not work like newer Apple Laptops so when you open the lid it will automatically turn on

Desktop computers are not Laptop computer and do not automatically turn on when you plug them into the AC ( electrical wall socket )

You can Schedule your Mac to turn on or off in Terminal

That, my friend, is outstanding explanation for OP to mull over 👍

Because it is a desktop divice isn't possible to achieve what you want, the closest thing would be to set a woke up-on time.