As far as I know you can't create republics or bishoprics vassals in vanilla CK3. We haven't changed anything here for the mod.
It appears that you can, and it works the same way as it did for CK2, with the additional complexity of county capitals, but otherwise it's fairly easy to do, I tested it a bunch of times in vanilla CK3 earlier today, and put up a post about how to do it on the main forum.
So knowing how to do it in vanilla CK3, I returned to my POD save from earlier and decided to try doing it there, but ran into some problems.
So in my POD save, I have a recently conquered county which has taken me over the demesne limit and I want to make it into a vassal republic. The county has one castle barony (which I own), and one temple and one city. Both the temple and city are held by rulers which have no POD splat. But here's the big deviation from vanilla and the reason I can't create a republic: both the temple and city holders have government type Traditions, which is why I can't create a republic. In vanilla, the city holder should have a republic government, and the temple should have a theocracy government type.
Is this normal in POD? Are all government types Traditions in a POD game? Because these two barony-tier vassals are both "human" (in that they have no POD traits at all, not Mortal, not Vampire, etc), and yet they have a Vampire/POD government type nonetheless. As a feudal Vampire lord, is there some script which makes all your vassals, all the way down to ALL baronies (cities and temples) automatically Traditions in government type? Or is it somehow possible for a Vampire lord to have theocracy and republic government types in vassals (and if yes, why are my cities/temples currently Traditions then)?
Also, I think I may have found an oversight bug in the mod: in vanilla CK3, you can revoke barony-tier titles at Limited Crown Law or higher, with no Tyranny. But in POD, if I try to revoke a barony title from someone, it won't let me because it says something like "You cannot revoke a title because their Vampire feudal contract doesn't allow it". But here's the onion: the POD mod won't allow me to alter a Traditions feudal contract with anyone of barony-tier, it only allows you to do it for Count-tier and above. So you're caught in a catch-22, and you can thus never, ever revoke a barony-tier title as a Vampire, which seems quite wrong to me. Is this a bug/oversight?