@Maltakreuz Sorry to hear you were having troubles, glad to hear you've figured it out. Normally the upgrade from RawImage to SkeletonSubmeshGraphic happens automatically, perhaps something went wrong due to separately applying the first commit and then the second commit.

After the GameObjects are updated, the prefab or scene needs to be saved, yes. IIRC the automatic update will be performed by editor scripting, so it likely won't be performed at runtime if you don't save it and build and run the game.

@Maltakreuz For sake of completeness: you could also use a Unity Sprite Atlas as atlas provider, as described here:
https://esotericsoftware.com/spine-unity-assets#Advanced-Unity-SpriteAtlas-as-Atlas-Provider
Note that this comes with some limitations however, and it would likely be better to use the Mix and Match workflow that Misaki suggested above.