It seems likely that this OccultPicker is hidden somewhere in Sims3Core. However, that can't be all there is to it. What makes the OccultPicker so special?
EP7 brings 4 SupernaturalTypes (witches, fairies, werewolves and vampires) + 2 Basegame (humans and ghosts) + 1 EP6 (genies).
I'm not really into coding, I can look at lists, but I can't do anything with the references through values, which is probably due to the coding.

So, with Supernatural installed, CAS displays seven options, one of which is greyed out because EP6 is not installed. Is the Djinn an EP7 LifeState that is only unlocked when EP6 is installed, or does the Djinn already exist as a LifeState in the game data with the Showtime patch/installation, and EP7 knows about it?
Similar to witches, however, the genie has no special characteristics, which means that a separate CAS menu is not necessary. The genie is visually painted by the game with an unnatural skin colour, without an overlay as with the vampire.
Ghosts and fairies get their own tab. If you edit a mermaid in CAS, they also have their own tab under Basics.

But let's get specific. In the Basegame...Game...Bin...UI directory, I took a look at the UI.package with s3pe. There is a file called CASBasic. Perhaps we can find a clue here. The menu item CASBasicsEP07:SupernaturalType is also found here. This is simply the heading on the user interface. It is followed by the comment ‘Supernatural Type Dropdown’ for the corresponding object that follows. This is followed by the buttons for the LifeStates, which are marked in the comment line as ‘Fairy Button’ or ‘Witch Button’.

The functionality has to come from somewhere. This means that the CAS reacts to the selected menu item. Where the placeholders and values lead to, so that they can be added to.
Unlike EP7 LifeStates, Mermaids have their own CAS files (CASMermaidSheet and CASMermaid). But that's probably something that coders will understand.

For me, the SupernaturalType menu is a list of links. Each entry is linked to a function that causes CAS to adjust itself. Whether it's the (terrible) vampire skin overlay, the switch to the second version of the Sim as a werewolf, or the additional menu under Basics for ghosts and fairies. The latter are no different from mermaids at first glance.
Simple way of thinking: duplicate the fairy button, change the link to the mermaid function call. This way, the fairy wings don't appear in the selection on the left, but the tab for the fin does.

Other missing SupernaturalTypes: Alien (like playable aliens, not NPCs), PlantSim (basically like the genie, in CAS it's a Sim with colourful skin and unlocked outfits, but with its own interactions), Mummy (like genie

Plumbots have their own CAS like pets. Plumbots can be called up using the ‘add new Sim’ function. So add a Sim, dog, cat, horse or Plumbot. Just an idea.

Just my thoughts. Would you be open to brainstorming?

I'm not a coder but does this sound like you're looking for a way to add more occults types that we can create in CAS?

I'm not a coder either and wouldn't even know where to start. I just rummaged through the files for references to this function.
It must be somewhere in the files, but the question remains whether it's somewhere in the programme core or whether it's modular. With the layout files, I've at least found part of the interface.
As I said, someone who knows about coding will be able to do something with the references in these files. Then we can work together to figure out how to integrate the other full-fledged LifeStates.

Expanding the occult catalog in the CAS was one of my desires when I had very little knowledge about script modding. I indeed worked on some UI stuff to make them appear in CAS, with no actual functionality.

To correct some misunderstandings and answer some speculations:

In conclusion, some stuff might be possible, but not without scripting.

Thank you for your contribution and experience with SupernaturalTypes. Interesting.
So mermaids basically have their own CAS, like pets and Plumbots do? Unlike werewolves, ghosts and fairies?

How does the Genie actually exist? Is it something that EP6 explicitly installs, or is it EP7 content that waits for an active EP6? Similar to how the weather stone is EP8 content, but waits for EP7?

Aren't aliens for Sims3 an occult type?

As I said, Mermaid CAS is to change their scale and bra colors, not to create new Mermaids. So it's not like CAP for pets and CAB for Plumbots.

Genie is not "installed". It's just locked if you don't have the Showtime EP, and cannot be created in CAS if you don't have the Supernatural EP either. Genie clothes, animations, etc., however, are content of the Showtime EP, meaning that even if you "unlocked" the EP restriction, you'd still need the said EP for the said content.

I think the Weather Stone object belongs to the Seasons EP. And yes, it's waiting for the Supernatural EP to emerge.

Aliens are not an occult type. Being an Alien is based on what percentage of a Sim's DNA is alien. Here's an example of how their reproduction and DNA inheritance work.

I've wished (wish in one hand, poop in the other and see which fills up first) I could create a new CAS life state, but have generally settled on using Nraas MC to give some Sims multiple occults, making them almost demigods... but a single occult would be cool.

Nraas MC isn't exactly an elegant game design. It is a tool. That's why it's all the more satisfying when someone figure out how these scripts work and that they can also be built around other SupernaturalTypes.

Oh, I totally agree. However, THIS little dress maker sees scripting and core mods as well above my pay rate. Hopefully, one of the script/ core modders will notice this thread and perhaps give you some info.

Ok so according to what's been said so far, adding new occults to CAS is technically possible but it would take someone writing the appropriate scripts?