I would title Part 1 as "Traveling to the Capital".
The big bad of Part 1 is Alkirk.
We are currently in Arc 2 of 4.
By the end of Part 1, it's extremely obvious that the nobility of the country is working openly with the demons and thinks nothing of their lives--our MC wants to tear the corrupt system down (Alkirk states that the demons are trying to control the human world from behind the scenes and the owner of the MC's childhood friend sees no problem with that).
I would title Part 2 as "Intrigue and Civil War"
The mage girl did "die". But there's something wrong with her spirit, so she doesn't "pass on". This enables the MC to "resurrect" her by MAKING HER A NEW BODY. She joins the MC's "party" (that term gets very loose in Part 2).
The sword saint runs away from home (while still handicapped) when her family starts talking about euthanizing her to make it so her skill can be awakened in another family member. MC eventually heals her and she joins the party.
The "hero" and the big guy end up kidnapped by demons who took over the human experiments after MC kills Alkirk. The experiments have progressed to the point that humans can now survive turning into demons (unlike the childhood friend who has to be put out of her misery by the MC). Both of them are turned into demons, but the hero takes to the demon power so well that he goes nuts and starts eating anything that moves (starting with the big guy). While the sword saint and mage girl encounter him while helping the MC, the fight ends due to the world-changing events at the end of Part 2 (a gate to the demon world opens church headquarters in the capital).
The little girl following the MC and the knight operating the gate in this town are eventually sent to train in Yggdrasil (for the girl, it doubles as protecting her from people who are after her). This is surprising because the knight is actually one of the villains of the current arc--he's the inside man for the werewolves, having given in to his anger at the world due to the kingdom's corruption costing him his family.
There are two big bads of Part 2--the King and the Saintess (head of the church)
The King is really a demon--one of the big 4 like Alkirk.
The Saintess is a bit crazy. If she didn't want to hurt the slave girl for some reason (I don't remember exactly why but she does have connections to the church), she would be the big good in this story.
I would title Part 3 as "The Demon World"
A big twist at the end of Part 2 is that while the Saintess and the King are both villains, they aren't true monsters because they don't recklessly endanger the lives of the civilians. While the MC is fighting the Saintess, the sword saint's brother teleports the King into the room, opens a portal into the demon world, and throws the MC, Saintess, and King inside (the demons in the demon world are noted to be stronger and more wild than the ones in the human world.
It's worth noting that the brother appeared once before in the series--not at the sword saint's home, but in the capital. He was the one who arranged the meeting between the MC and the noble who owned his childhood friend (where the MC ended up fighting Alkirk).
Another time skip happens. The church & kingdom armies were basically destroyed by the civil war and the demons pouring out of the gate (for some reason, demons can come through that gate to the human world but the MC can't). Since the gate is still at least partially open, the capital was abandoned. The people who survived were saved by a mysterious new cavalry, CONVENIENTLY led by the sword saint's brother.
The slave girl and knight finish their training inside Yggdrasil and meet up with the sword saint & mage girl to try to find a way to bring the MC back from the demon world. It's not clear how many holy knights survived--the ones shown in Part 3 so far were already supporting the MC in the war (this group is featured prominently in Arc 3 of Part 1 and witnesses the collaboration between Alkirk and the nobility in Arc 4).
It turns out there are factions within the demon world. There is a "peace with the humans" faction that includes the King and most civilian demons, a batshit crazy faction that wants to slaughter all the humans and actively kills any demon who doesn't believe the same (the strong & wild demons in the demon world are in this group), and a "neutral" faction that Alkirk was in that just does whatever they want.
A surprising new character is introduced--the hero who killed the demon king. He's been in the demon world since he killed the demon king, having joined the "peace with the humans" faction to keep them from being slaughtered (the late demon king was in the crazy "kill kill kill" faction).
And that's about it. I would say we are maybe a third of the way into Part 3, based on how long Part 2 was.