Stage One:
Research Esoteric Technology
Wait for Project
Do Special Project
Get Reward

Stage Two:
Research Psionic Theory
Wait for Project
Do Special Project
Get Reward

Stage Three:
Acquire Psionic Ascension AP (PSIONIC TRADITION NOT NEEDED!)
Do Special Project
Get Reward

For most projects the reward is just a new Civic and an Empire Modifier.
Civic is usually based on fanatical ethic.
Each Civic is part of a set of 3 and usually provides 4 modifiers.
The Empire Modifier is based on your current Authority.
Each Project provides a new civic in the set and empowers them to provide stronger modifiers. Also upgrades the Empire Modifier.

Instead of 4, these provide 6 modifiers.
Neutral, Purifier, Exterminator, Devouring Swarm, Devouring Lithoid all have their own sets.

For Machines, they get a set based on which of the 3 civics they have (or if they have none)

For Hives, the player gets to choose a "Personality"
These are based on ethics usually:
Aggressive - Militarist
Cautious - Xenophobic
Cooprative - Pacifist/Xenophile
Curious - Materialist
Introspective - Not Based On Ethic
Expansionist - Not Based On Ethic
Productive - Not Based On Ethic


After you finish the first 2 Special Projects, you must take a Psionic Ascension AP
This is NOT related to the Psionics Tradition at all. You can use any traditions you want with this. This AP will grant immediate access to a new Special Project that allows you to ascend and gain a new portrait if you wish and a new trait. As well as granting the 3rd and final civic of your set and empowering your previous ones.

Some years after completion, you will get a choice.
To meet an NPC, Learn about the universe, and partake in a story. With upgrades being gifted at various completions of the story.
Or you can go down an alternate path, the standard, research, gain project, do project, repeat. These technologies do not do anything on their own however as those following the story path would not have access to them. Either way you will be directed eventually to a new Psionic System. Following the story and/or settling one of the worlds will lead to the end.

Each project usually unlocks new techs. No weapons or components, but things that provide a variety of minor stat boosts.
Admittedly rather limited currently, I want to heavily expand on tech once I know what I have works and is paced good.

You will have access to at least 1 Shrouded World naturally as the game progresses but you can make more via the acquisition of an AP and subsequent activation of a decision to Shrouded a world.
Yes these are compatible with Psionic Worlds from Planetary Diversity.
Shrouded worlds start with just City Districts, but after colonizing them, the player can choose a decision to form new districts to build on it. Shrouded worlds can have 4 districts of the players choice.

You can also get Shrouded Ringworlds and Habitats but these do not have customization support yet.

Shrouded Worlds are essentially Hive/Machine worlds, providing buffs and resisting invasion, but being customizable.

Spoilers for the end game below:
If you Contain the energies you will gain access to a customizable Megastructure, allowing you to choose which resources you want it to produce.
It also produces more depending on how many AP you have.
In your edicts menu you can find the ability to change its produce.

Random Boons

You will find another Edict that allows you to apply a boon to either planets/ships.
This boon is random in what it will do. 5 potential boons can be applied chosen at random.
Or you can have a random boon/malus applied to your Friends/Enemies.
This cause those friendly to you to gain a boon and those with negative relations to gain a malus. These are the same as applied to the player, for enemies the effect is reversed.

Temp Fleets

Or instead of boons, You can instead choose to summon an allied fleets temporarily. These last 5 years but are... Possibly OP.

Charging the energies grants you similar things as before, but with more control and power. The trade off is you miss out on the Temporary Fleets and the Customizable Megastructure.

Controlled Boons

In Edicts you can apply boons/maluses. But these are slightly more powerful and the player has control over which boons are applied.

The Ship/Entity

Charging gains the player access to a Single Very Powerful Ship.
This ship may not be as powerful as the fleets you can summon, but in testing it has single handedly defeated most of the Leviathans I put it up against with the exception of the Automated Dreadnought.
I plan on making it more powerful via techs. If the ship is ever destroyed, you will gain a powerful boon for a year and whatever empire destroyed it with gain a strong malus for 1-3 years.
You can find an expensive edict to respawn the entity if it dies.