From my observation of the "Genesis" Awakeners so far in Morimens, they tend to lean closer to what their source mythology is than the first version of them did and often more dangerous/more of an enemy due to them being more 'eldritch' like their source.
Examples from what we have so far being...
Doll- based off of Mi-Go, G!Doll has at least ONE confirmed case of putting another person's brain in a vat for study and storage like the Mi-Go are infamous for doing instead of storing only her own brain like normal Doll does. Also, the machine that she uses to poison you in her Boss Fights in Arc 2 looks a lot like a Mi-Go as sketched out by later artists. Mi-Go have a very alien moral system like Doll Inferno has, making them (and her) malicious to the human experience.
Murphy- based off of Cthylla, who is both the daughter of Cthulhu and births Cthulhu. Her Genesis version, Fauxborn, manages to do both as the mythology claims by giving birth to the False God who then in turn supports her Silver to be Awakened (as stated in her Story material). Her pale coloring also seems to match up to some art I've seeing of Cthylla specifically, though it is Original Murphy whose coloring that actually matches up Cthylla's description in In His Daughter's Darkling Womb.
Ramona- Now, Ramona is a touch more tricky, seeing how her origin story is basically a human that was heavily touched by an Outer God/Old One. BUT Timeworn Ramona very much takes after the Outer God that Tawil is based off of, Yog-Sothoth, which is a being that exists outside of space and time. Genesis Ramona exists in a space where she can pretty much always come when called to assistance by the Keeper, much like Yog-Sothoth's name is called upon in several Lovecraft stories for similar protective purposes. Her eye covering might be alluding to how Yog-Sothoth is also said to 'know all,' an attempt to limit knowledge that she is always being immersed in at her current locale.
SO, for future Genesis Awakeners, my bet is they are going to tie them even closer to their source materials as well and Genesis Tulu is going to be even MORE like original Cthulhu, thus being a monster in truth than a young king alone.