Construction costs are currently skyrocketing

Instead of looking at any twitches in the graph, I would rather ask for reasons for a trend reversal. If there are no good reasons, one might not come. In the short term, I see more reasons for the opposite.

There are none either. What the ECB decided for September does not affect construction interest rates at all. As other forum members have already pointed out, German government bonds are currently at 2.4% and had risen from below 2% to 2.54% in June. It is said that the construction interest rate is the interest rate of the government bonds + 1.1%. That would be 3.6% as of today. At Interhyp, the 15-year interest rate rose to 3.57% today. If there is no significant increase tomorrow, it will probably stay at 3.6% for the time being. If the ECB continues to buy southern European bonds, then ours will continue to rise.

Interest rates will fall due to the aging population. This problem affects all industrialized countries. The older the population, the greater the pressure towards lower interest rates. Therefore, the increase is only temporary. When it will fall again is, of course, still uncertain. Older people consume less and invest more. The historical increase in the past could be attributed to the Baby Boomers who caused the exact opposite.

Interest rates will decline due to the aging population. This problem affects all industrialized countries. The older the population, the greater the pressure toward lower interest rates. Therefore, the increase is only temporary. When it will fall again is, of course, still open. Older people consume less and invest more.

Quite possible, you can take Japan as a role model.
Old, heavily industrialized, and highly indebted – for decades. But it will be interesting to see whether they can manage the currency crisis there.

The interest rates will decrease due to the aging population.

?? Then they should never have risen in the first place :) I don't quite understand the logic there.

Aging population means that the proportion of older people within the total population is increasing...