All the cult leaders who claim to be God/Jesus never have any powers. If I join your cult, and you claim to be Jesus, you'd be better be ready to do some magic.
And you can equate religions and cults because the only difference between the two is time.
There is more difference than time. Cults require a charismatic, authoritarian leader, religions do not. One can be religious and autonomous in practice.
Religions can be open source and decentralised, cults cannot.
When discussing American furniture, I like to refer to the Shakers as a "sect" and not a "cult" because as far as I can tell they didn't commit any atrocities.
At least both Christianity and Islamic religions started as cults and became religions. Christianity was even a sect of people believing in the coming of the end times, that's what the revelation in the new testament is for.
A sect or a cult is always the root of any new religion and often new sects or cults are the offspring of an older religion.
Religion, cults and sects are as concepts interconnected.
My favorite example of this is the idea of money and finance.
There are trillions and trillions of dollars worth of imaginary wealth everywhere. None of it can be backed by actual product or material .... it all exists because we all collectively believe that it exists.
It's our modern day religion and we all believe in it and worship it daily ... All Hail Money!
As authorized by the House of Apostles of Eris, I'm a card-holding genuine Pope. So are you and so is everyone who reads this message, if they so wish.
That's not how cults work. They are made up of ordinary people. The leader abuses human nature and gets people to do crazy things. The fun thing about being in a cult is that you don't know your in a cult.
There is a fun Netflix documentary where a guy creates his own cult: Kumare.
In the end he feels bad for taking advantage of peoples’ trust particularly when vulnerable and has a semi-sincere apology for including them in his project.
So the first requirement is you need to be a bit of a sociopath or a true believer (aka a bit crazy)
Not if "believe" from the followers is some kind of cosmic energy that powers the gods or defines their hierarchy, a pandimensional twitter subscription counter of sorts.
In that case the last thing you want is to prove your existence as a god, because as soon as your existence is proven all believe will pop out of existence and will be replaced with knowledge of the existence.
Believe is only possible when the thing to believe in is vague and unknowable, you can't by definition ever believe in the existence of anything that you are sure of.
This is why claiming to be a "prophet" (by any of a multitude of definitions) is so popular for cult leaders.
You can say you have information from a deity, one way or another, or even that you get special treatment from a deity. No special powers needed. If people believe in the deity and they believe you were chosen by that deity, to counteract that would mean counteracting the belief in the deity itself.
Extremely relevant video of Derren Brown, British illusionist: Miracles for Sale - It's very easy to pretend you have some sort of miracle healing powers.