I don't think it is considered pseudoscience, but to the extent it's not pseudoscience, it is simply a mechanism of diffusion.

>I just want to know if there are other accepted frameworks other than diffusionism and evolution.

There is, but not in history. You might be thinking of divine revelation, in which case you should try some theology subs.

I'm saying that there are a limited number of regular geometric figures available in the universe, so that will cause repetitions in their use. Also, that physics is the same everywhere, so that also limits options. I think the two main frameworks you cited are enough to answer the question. Unless you want to start thinking about divine revelation, which is also widely claimed by ancient peoples.

I suppose geometry and physics are the same everywhere at any given time. That could explain most "coincidences".

"The god in monotheistic religions is the (body-less) embodiment - or the very definition - of what is right."

Yes, I believe that is a fair description of monotheistic theology.

"In Greek and Roman religions, the gods are pretty much just humans (with both human virtues and failings) with superpowers."

Kind of yes, but not really. I take polytheistic gods to be embodiments of *some* aspects of perfection.

In a monotheistic religion, all those aspects are united in a single being. When we talk about "Elohim", for example, we are using a plural word that to some people, means the unification of all "El" (can be translated as power) in a single being. It's like they took all of the deities that each represented one aspect of perfection and merged them together into a single being that possesses all aspects of perfection and, therefore, cannot lack it in any way, thus being perfection itself.

"But how did their stories relate to anything going on down on Earth?"

Their stories convey lessons related to that aspect of perfection that they are believed to embody. A god of war, being the embodiment of a perfect warrior and of the perfect way to wage war, cannot be also the embodiment of a perfect musician, and his story will reflect the lacking of those perfections, sometimes as a way to emphasize the perfections related to the god, and sometimes to emphasize the imperfections that are taken to be normal to a warrior.

"And why would any power derived from them give you any authority over other people?"

Again, through examples. If you are in a situation in your life where you need to be victorious, you go to the temple of Nike in order to learn about victory itself. If you need to get married, you look for a temple of Hera and learn what you need from the stories told about her. If you wish to be a good musician, you look for the servants of Pan. And so on.

Many gods were patrons of specific professions and their followers were the experts in those fields. If you wanted to become a successful blacksmith you were bound to seek help from a follower of Hephaestus.

"What did Greek and Roman priests even do? And why?"

They kept a tradition related to the role/nature/perfection related to the god they served. They kept oral traditions, books, and rituals (that are usually theatrical demonstrations of principles applicable to the perfection they served). They collected sacrifices and used them to fund the entire operation of keeping a place that must serve many generations and be a hub for the study of a particular aspect of reality.

I welcome any correction to this way of understanding it.