This could actually be fairly straightforward since these already exist for dictatorship, you'd just have to unlock them by altering the PathPrerequisites for the other governments.

In ConstructibleElement_Industry[StarSystemImprovement].xml which is found in C:\Program Files (x86)\Steam\steamapps\common\Endless Space 2\Public\Simulation, you can find these improvements by searching 'propaganda'. The top one is like so:

<StarSystemImprovementDefinition Name="StarSystemImprovementPropagandaPolitics01" SubCategory="SubCategoryPropaganda" >
<Tags>NoBuyout</Tags>
<InProgressSimulationDescriptorReference Name="StarSystemImprovementPropagandaPolitics01"/>
<ConstructionQueueEntityActionReference Name="Politics01PropagandaSystemAction"/>
<InfiniteCost ResourceName="SystemTurnBased"/>
<SupportPrerequisite Flags="Prerequisite,Discard" Politics="Politics01">1</SupportPrerequisite>
<PathPrerequisite Inverted="false" Flags="Prerequisite,Discard">../ClassEmpire/GovernmentDictatorshipCommon</PathPrerequisite>
</StarSystemImprovementDefinition

If you remove this:

<PathPrerequisite Inverted="false" Flags="Prerequisite,Discard">../ClassEmpire/GovernmentDictatorshipCommon</PathPrerequisite>

You'd also have to remove:

<SupportPrerequisite Flags="Prerequisite,Discard" Politics="Politics01">1</SupportPrerequisite>

to unlock all of them, not just the leading party.

It should then always appear, or you can define which other governments you want it to appear for. You could also add a new tech if you wanted to Empire Development to unlock access to these for the other governments by setting a TechnologyPrerequisite and then an inverted PathRerequisite that locked the new one from Dictatorships.

Do you want it to be the same as the dictatorship one, worse, or better? The value is set in EntityActions[System].xml as below:

<PropagandaSystemAction Name="Politics01PropagandaSystemAction">
<SupportPrerequisite Flags="Cancel" Politics="Politics01">1</SupportPrerequisite>
<PoliticsDefinition Name="Politics01"/>
<PoliticalScoreGainFormula>Clamp(2 ^ ($(Duration) * 0.5), 0, 200)</PoliticalScoreGainFormula>
</PropagandaSystemAction>

If you know what you want to accomplish I can help you put it all together like that. :)