Should we buy an overpriced property?

What happens if market prices suddenly crash? You simply continue to pay an installment that is absolutely manageable for you and have no other disadvantages. And you live in your dream house.

It only becomes bitter if you have to sell.

So is it normal that the appraised property value by the bank is often lower?

Yes and no. There is the market value / fair value and the lending value. The lending value is always below the purchase price (except maybe in favorable purchases within the family). The market value is also an automated valuation. A machine generally looks at the standard land value and, based on key data (area, year built, condition), estimates the asset value. This is an approximation, nothing more. Not a "real" property appraisal.

What we don't like is that the price is about 20% above the market value!

Your description, however, sounds as if "only a 20% markup" on the market value a) is absolutely a bargain and b) relatively the best offer that awaits you within reach; c) otherwise, I see you searching for another five years. A price-value ratio of 1.2 : 1 is relatively cheap in an overheated market. In addition, I read the note

Small consolation is that there is no broker yet.

as a signal to hurry before the seller gets any foolish ideas.

Just as a side note. For capital gains tax, the period is 3 years (07/21 - 01/23 is also 3 years)

Rented out = 10 years. Owner-occupied = no time limit if you have always lived there (also purchase six months ago and sale today) or time limits if it was rented out before owner-occupation.

So is it normal that the appraised property value by the bank is often lower?

Yes, that is normal. Banks conservatively assess a guaranteed resale value for them just in case. The purchase price (= market value) has nothing to do with that. If you want to determine this, then get an appraiser for 300-500€ who will inspect the property and then provide a price estimate.

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