Should we buy an overpriced property?

Yes and no. There is the market value/traffic value and the lending value. The lending value is always below the purchase price (except maybe for cheap purchases within the family). For the market value, it is also an automated valuation. A machine looks generally at the standard land value and estimates an objective value based on framework data (area, year of construction, condition). That is an approximation, nothing more. No "real" property valuation.

You must not worry about the lending value at all; otherwise, you will start doubting the whole topic of building/buying a house. Land from the city and still the unsecured portion of the loan was over €70k, even with €100k equity. There was no item not assigned to the house construction. If you now assume that others build on market-value usual plots… manoman.

Ever thought that the seller might enter a bidding process with you after feedback from all the interested parties? Then it means 20% + x%. If the area is in such demand, then the likelihood is high that it will happen.

So, it means don't wait but grab it :-)

We also just bought overpriced (but I don't have a percentage at hand).

Does it annoy me to have paid too much? Yes, because a lot was just botched and the previous owner was generously rewarded for it.
Does it annoy me THAT we bought? No, because: We have a house! We are going to make it nice now, and as the botched work is gradually fixed, the annoyance will fade.

We actually didn't even negotiate the price because we had gotten burned too many times by doing so (negotiating too long, negotiating at all, we just kept getting outmaneuvered). We had them do some work (cleaning and painting the facade), but nothing more.

Unfortunately, we had an agent. I'm annoyed about that too, €15,000 for nothing. At least you can save that!

One must not worry about the lending value at all, otherwise one gets doubts about the whole topic of house construction/purchase.

Anecdote from my usual financing routine. New construction multi-family house in a good location ==> lending value corresponds to 16 times the annual rent. Construction costs are maybe at 23-25 times the annual rent. Market value at 35 times the annual rent. 100% financing when buying = 55% equity required + additional purchase costs from equity. The valuation in the simple single-family house sector is quite manageable.

Unfortunately, we had a realtor. I also regret that, €15,000 for nothing. At least you can save that!

Realtor, one of the most useless jobs ever :-)

Basically, you are saying it yourself: if you know that there are significantly more interested parties and you even think they would pay more => then the house is simply not overpriced! The bank's assessment is just conservative, which it has to be. If everything fits for you, then you probably shouldn't wait too long. Alternatively, you can ask the [Gutachterausschuss für Grundstückswerte] for information from the purchase price collection. If there have been comparable sales, you can see what was paid. However, this takes time!