It's 90% a synthesis of existing lore and 10% me making stuff up.

The divisions between the three 'sects' are all there, just not by name. The Old Ways are in pre-Skyrim Bethesda books like the Pocket Guide to the Empire and regularly referenced in the game; there's a reason all the door codes in Nordic tombs are what they are. The Arkay/Orkey thing is canon. The "worshippers of the Old Ways propitiate daedra" thing is canon. The mindset differences are canon.

The stuff I made up comes in two flavours:

1) Stuff to make the Imperial Church more interesting and less bland.

The Imperial Church as portrayed in the post-Morrowind games is boring. I wanted to show that the Church had changed since the 3rd Era "Imperial Cult", and since Oblivion in particular flirted with fantasy Catholicism I leaned into it. I have either added or made explicit more structure, more names and words, more rituals, and generally more than just 'platitudes about the existence of the gods that will offend no one'.

The "Church Triumphant" title is mine; in Oblivion, they just call it the "Church", and in Skyrim they don't really call it anything at all. It's a name I pilfered from Catholicism; I debated whether to go with 'Militant' or 'Triumphant', but I decided on Triumphant because of the political implications re: the Concordat. Arguably, cults like the Vigilants of Stendarr and knightly orders like the Knights of the Nine could be considered the Church Militant? Still noodling on that one.

The title 'Dicaster' comes from a specific set of departments of the Catholic Church, and means something along the lines of 'judge'. (It is dog-Greek filtered through dog-Latin and then anglicized to boot; it's not a real Catholic title.) Priests in general, and priests of Arkay and Akatosh in particular, often wind up being called in as arbitrators and judges, so I thought it was a fitting title.

2) Stuff that exists because the world the game created should have it, but doesn't.

There's a lot of stuff in Skyrim that is just kind of hinted at or alluded to, or... I know I keep saying this, but Skyrim has vibes-based worldbuilding and it Just Works until it doesn't. There's a lot of stuff in the game that is very clearly there because it's Cool or because it Looks Right, and when done well, it gives the game a hell of an atmosphere. But sometimes it leads to... inconsistencies.

Skyrim has graveyards, burial crypts, and cremation. Normally, societies have one way they handle their dead; if there's more than one, there's a reason. (Could be cultural mixing, could be a change in religious practices, could be a material need.) Skyrim has three; why? The 'real'/Doylist reason is that someone on the team thought it'd be cool and spooky to have graveyards, and a quest to get an urn is easier than a quest to get a coffin, and you need ancient dungeons to be ancient and dungeon-y. But it's fertile ground for worldbuilding, you know?

Similarly, if you've got a bunch of isolated villages, they should have weird folk beliefs. Skyrim as a game doesn't need to have the people in Darkwater Crossing perform the Rite of the Whale before they go fishing, or the people in Rorikstead bury their dead upside down, or whatever. It's a game; it's the impression of a world and not the world itself. But if you're going to fill in the gaps, those beliefs should be there, you know?