Circulation pump - 10 seconds until warm water arrives

Yes, but time-controlled, 3 times a day on for 30 minutes

Yes, 300 liters storage

Ok, once every 8 hours. Then it is clear that after 7 hours hot water cannot come immediately, it has cooled down.

Even though it runs 24 hours a day, hot water does not come out immediately but only after 5-10 seconds

I tried both with and without time control

Is it the same at all dispensing points in the house?

As the word circulation already says -> That is a cycle. From this cycle, the pipe to the faucet branches off. Depending on how long the pipe to the faucet is, the effect you described is stronger or weaker. It is also not automatically the case that all withdrawal points are connected to the circulation. You first have to check that. For example, in our case, the guest toilet is also not supplied by the circulation pump.

As already mentioned, I received the following response from the plumbing department: Even a circulation line must be connected at some point. This cannot be done directly at every outlet. Consequently, a small section of pipe remains in which there is no circulation water. I think that makes sense. The circulation line goes to all outlets (3xDG, 3xEG, and 1xKG). This also aligns with your statement.