There are many different types of power.
For example I have ideas for a character who has no special powers except for their intelligence. They are sent to various places and times and various situations, and use their intelligence and whatever tools, weapeons, etc. they have on their person to affect the course of events. And whenever they are killed, they are given new body.
So suppose that their enemies defeat and kill them. Sooner or later they will return to that place in another body. If they appear there later in history they can study the history of their defeat, and also learn about the ancestors of their enemies. And if they later (int their timelien) appear in that world or place at a time earlier than they defeat, they can take steps to prevent it in as many alternate universes as possible, possibly by killing an ancestor of their enemy, and thus making that enemy never born.
Thus they are certain to win in the end, but how much they enjoy or suffer getting to that end can be highly variable. And when they find themselves in the same situation over and over again, their goal is to improve their technique each time to do as much good and as little harm with as little effort as possible.
So in one sense they have omnipotent, since they are certain to win in the end, but while they are actually in a conflict they are in real danger of a temporary defeat and suffering.
So it is possible to design a character with the attributes needed to always prevail in the end, but who have the potential to suffer and be defeated on the road to ultimate victory, if they don't think of and use the correct strategy right away.
And think about an omnnipotent character like Superman or an omnipotent god.
The thought has occurred to me that all such hyperpowered characters may be sissies.
"What, sissies!" you say. "They calmly let atomic bombs they ae sitting on explode, they calmly walk through dragon fire, they never show fear. They are the bravest of the brave."
Bravery is facing your fears. Fears of danger. If nothing is dangerous to someone, they have no reason to fear anything. If nothing they choose to do can be dangerous for them, they cannont choose to face a danger they are afraid of.
So an invincible and invulnerable character can't be brave.
And whether they are a sissy is a little bit harder to discover, since there isn't anything for them to display fear of and so show that they are a sissy. But certainly if someone was always invincible and invulnerable they never had any fears to face, and so never practiced facing their fears and being brave. And I suppose that even the sissiset sissies sometimes practices facing (some of) their (presumably lesser) fears, so someone could claim that omnipotent, invincible, invulnerable people must be more sissies than even he sissiest ordinary person could ever be.
So a superperson could be embarassed by being called a superhero, since they don't have any reason to believe they are being brave when they face things which would be dangerous to mere mortals.
So one aspects of really powerful, invincible, and invulnerable characters who have been that way all their life instead of gaining their powers years after birth, is that neither the writer, the reader, or the characters themselves can know whether they would be superbrave or super cowardly without their powers, and it might not make the slightest difference to the plot.
But if the super characters are actually sissies, it can be a part of the plot. Maybe they would not only be afraid of their version of kryptonite if they discover they have one, but maybe they find it really hard to face any violence, even if it happens to other people. That would go a long way toward keeping a superhero from turning into a supervillain. But it might make them hesitate to stop a crime in process.
And maybe they can't stand to hurt anyone, and so they constantly try new methods to defeat criminals and supervillains without hurting them. Maybe they can't stand it when other people are in pain or are scared, and so find it hard to rescue accident or crime victims. Berhaps their heroism lies in forcing themselves into situations they find highly disturbing in order to save people from trouble.
Maybe they constantly desire to retire from being a superhero and are constantly afraid they will stop being a superhero and let innocent people die.
Or maybe a supervillian stops his career of crime after making themself rich or powerful enough to satisfy even him, and tries to enjoy life without all the stress of being a supervillain. But they find their retirement troubled by fears of being punished by superheroes and keep creating super defenses against such a possibiity and still constantly worry.
And maybe a powerful god will get bored with everyhing going so easy for them, and think about putting themselves into situations where they can't use most of their powers, situations which would be dangerous and exciting and would end their boredom, but they are too much of a sissy to do anything that dangerous. And so they have a constant mental conflict.
in the Star trek: The Original Series epsiode "The Changeling" there is the following dialog about Lt. Uhura:
NOMAD: That unit is defective. Its thinking is chaotic. Absorbing it unsettled me.
SPOCK: That unit is a woman.
NOMAD: A mass of conflicting impulses.
That dialog is often considered sexist against human wome, but it can also be considered to be speciesist against all humans of any gender. Or it can be considered to be quite accurate about all humans.
Unless your superheroes, supervillains, demi gods, demons, gods, or other superpowerful beings are also super consistent and well organized mentallly and emotionally, they are as likely to be "a mass of conflicting impulses" as any humans.
Which means that there would always be the possibility of dramatic conflict between them an other characters which they wouldn't have the power or will to resolve using their superpowers. If you really love someone, will you use mind control on them to make them think and act the way you want them to? And always the possibility of dramatic conflict within them, as they struggle to decide what to do with thier lives and their powers.
I think it has been about sixty years or more since Marvel Comics first had superheroes with super inner conflicts, so that is not exactly a new idea.