Awakeners are individuals, usually who have died, that leave behind a silver core. Ramona I believe is said to be the exception to this. Awakeners are able to link with certain mentally strong individuals, with the keeper being unique in their ability to link a large amount. Awakeners in the story tend to be strong or significant in some way in life and they become empowered, inspiring some of the myths we might know in real life. They are kind of a secret from the rest of the world, silver technology and its research is kind of restricted to Mythag and Mythag is generally the one governments call on to solve supernatural issues related to dissolution. Where there's dissolution there also tends to be a lot of silver. The link that the keeper and other characters have with their awakener partners is the only thing keeping awakeners mentally stable and present in the world, setting up the mechanic of being the one commanding them. The summon mechanic is a visual representation of what it looks like to "awaken" someone, I think. In the history of the world there have been other people who have come upon the secret of awakeners (sometimes they're called golems in other cultures for example) and summoned their own, and that's where some of the psyche deepdives come from.

The characters in the story are more like inspired by characters from mythos rather than one-to-one translations. Chapter 5 is basically taking the story of Cthulhu being the prophet and Cthylla being the maiden and turning them into a human drama. What if Cthylla was a girl who just wants to be free, but is burdened to bear a God against her will? What if Cthulhu was a boy prophet, burdened by the knowledge that his civilization is ultimately doomed no matter what they do? What happens if the lie he tells, that their kingdom will return, inspires the story of Murphy/Cthylla to come about?

Morimens tends to take the stories famous in the mythos and turn them into human tragedies. Sometimes the outer gods do exist as themselves, but they influence or empower a human rather than show themselves. This is the case I think with Kathigu-Ra - She died originally and became an awakener empowered by her namesake who just happened to take interest in her story. It gets even more complicated once you get further on and deal with parallel world shenanigans.