Pretty sure you got as far as I got in Klaus route, which is day 2.
Jorgen route has an appearance of Klaus doing some art project in the city during day 3 (iirc) which means that at least in the non-route timeline Klaus does that during day 3 but I haven't found a way to reach day 3 with him
The fact that he goes to Dan's hut regardless makes me think that his actions are the same in route and non-route timeline, and the fact that is day 2 has neither credits not the normal "work in progress" text makes me think it's a sort of reset mechanic where you have to do something right to get the route using the lead he gives you. The problem being the missing piece between the roof of the guesthouse and the city.
That or the same is true except Klaus' route isn't updated, which would be a shame since it's been a long time