Does the architect fulfill his contractual obligations?

The architect has prepared execution plans (service phase 5) and specifications (service phase 6) and sent them to me.

Well, at least - so far I had the impression that instead of service phases 5 through 8, he only performed service phases 5 and 8.

The construction schedule was prepared relatively late (after installation of the windows)

You should have at least declared acceptance under reservation by then; actually, a demand for performance should already have been issued long ago.

I do not receive any ongoing cost overview,

The cost funnel is long outdated in service phase 8.

I am now interested … does the architect formally fulfill his duties and I end up paying almost €10,000 solely for service phase 8 just because he occasionally took photos with his phone? Or am I entitled to more documentation?

I see an entitlement only to a construction diary. However, photos are not part of that, as the habits of homebuilders blogging about construction have advanced considerably beyond the duties of architects. I see your expectations rather in service phase 9 (which, in my opinion, is not reasonable for a single-family house).

After 3 months I learned that he has a 30-hour position at a large architecture firm and additionally has other obligations.

However, I would consider this also worthy of censure by the chamber if he did not inform you about his secondary self-employment before signing the contract. From my point of view, it is covered by "good faith" to assume, as a non-merchant client, that an architect is freelance self-employed at least as a main occupation without special notice; under these conditions, I would even consider the expectation that he is exclusively so not exaggerated. In this respect, I thank you for the suggestion to include this in my architect contract tips.