How I find a house that suits me within an appropriate timeframe

I read that you have a 101% certain counter-position to almost all the suggestions here without exception, or you rhetorically bring almost all the proposals to their knees or portray them as non-functional or inappropriate.
That alone is nothing reprehensible, but I wonder why on the one hand you seem to brim with knowledge and argumentative certainty and on the other hand you are a help-seeker who apparently has no obvious goal-oriented idea at all about how or where to get the best house for yourself and where or how you can live in the future.
Maybe you should first say something about the background, why exactly no longer NRW, what family situation, professional situation, family, personal life plan, etc., because these seem to me rather the overarching search terms in such an important matter; the house has to fit your life and not the other way around.
And......if you do not see hints here more as an incentive to think about your position and the house topic from another perspective, you miss the chance to learn something for yourself.

You are using the wrong word. You don’t find my statement funny.

Thank you very much for this insight. I am starting to find you funny – or entertaining? Help me. What do I actually find? Apparently, it is not worth contributing to the matter. Good luck.

I have the opportunity through an inheritance to buy a house for personal use up to a maximum of €500,000. I have written down some personal criteria concerning the surroundings of the house. For example, supermarkets should not be farther than a certain distance, the next larger city should be at most X kilometers away, and the next airport should not be too far away.

So, considering the thread, I can only give you one recommendation. Since you are very rational, you naturally don't trust the temptations of fiat money. Since you are unemployed with €500,000 in the account, I can only advise you to go out today and buy a motorhome in cash. Along with that, a map of Germany with a dart. Your schematic procedure starting today: a) Now you mark your airport radii b) and then just throw darts until you hit the first catchment area. c) You drive there tonight and look for a free parking spot. d) Then you explore the area for at least a week. Repeat from b) Every five repetitions, write back here again. Then continue from b). The total number of repetitions is based on the number of posts in this thread, so you have a perfect feedback loop. e) Buy a house in your determined region. Formula at the end of the thread.

A systematic approach could also include following up on the tips already given and reporting one's success from this measure.

Just enter "11ant Barthel" in the forum search, then you should be able to find my related tips.

It looks as harmless as a single sentence, but basically leads to a whole toolkit of systems on how to proceed.

If the first house in the Harz is too small for you, here is another offer. If these aren't dream prices...

If the first house in the Harz is too small for you, here is another offer.
If these aren't dream prices...

Amazing, here you can barely get a 60 sqm apartment for that.