Strategy for selling a house - what is the best way to proceed?

The notary takes care of legal security and liability disclaimer in the purchase contract.
The real estate agent may know someone, but I strongly doubt that he can make a good preselection based on that. Good agents can do that more through experience.

What speaks in favor of a real estate agent is avoiding the effort. That can be worth something.

That’s true. A real estate agent who “advertises” with something like that would be out for me immediately. I have a real estate agent whom I have to hire professionally quite often, and he has never told me such nonsense. And I consider him reputable.

Furthermore, he said that through his connections to banks he could also make a more precise pre-selection regarding the creditworthiness of buyers. I was surprised by the statement (keyword data protection?), but I wonder if there might actually be something to it.

The (banking) industry has quite effective instruments, formally compliant with data protection law, to pay no more respect to data protection than is conducive to business success – besides, there are (except for taxes) nowhere more anti-data protection laws than in the banking sector ;-)

We will hear an exact price estimate next week. It makes a serious impression on me that he doesn’t just come up with one on the spur of the moment.

You really don’t want to know how long he has practiced this drama in seminars and in front of the mirror ;-)
As I said, I expect a price above what you paid.

Legal certainty and liability disclaimer are handled by the notary in the purchase contract.
The agent might know someone, but I still strongly doubt that he can make a good preselection based on that. Good agents can do that more through experience.

What speaks in favor of an agent is avoiding the effort. That can already be worth something.

Okay, I had somewhat suspected that the legal certainty was hot air. He was (of course) a talker, but that's an occupational disease for them, I didn't expect anything different.
I also don't know if the pure amount of work he takes off me is worth over 20k euros.

I also wonder if a price of a certain amount has a higher chance of being achieved if the property is listed via an agent rather than if I, as a private person, would list the same price. Of course, it would be cheaper for the buyer via private, but whether they perceive the price – purely psychologically / emotionally – as equally appropriate when I, as an amateur, call for it, compared to calling for it via a "professional," I doubt that a little bit. If you understand what I mean?

The (banking) industry has quite effective tools, formally data protection compliant with not one milligram more data protection to observe than is conducive to business success – besides, (except for taxes) there are no stronger anti-data-protection laws than in the banking sector ;-)

You really don't want to know how long he practiced this dramaturgy in seminars and in front of the mirror ;-)
As I said, I expect a price above what you paid.

I’m kind of expecting that too. I also tried the company’s online calculator once, those things where you enter the address and a few details and it spits out a price. The online calculator came up with a range of 495-630k. If we land anywhere in that range I'm quite satisfied. If we have a 6 in front, we’ll buy my husband a Tesla. :p :D

On the one hand, it was about legal certainty and disclaimer of liability.

He will exclude all liability for himself and, anyway, will always fall back on the position that you are responsible for everything he tells potential buyers. That was, for example, one of the many reasons why we wanted to sell without an agent. No control over what he tells the interested parties and if there were later difficulties, we would have the problems and not the agent.
Furthermore, in my opinion, the risk of conflicts and problems increases the more people are involved in a legal transaction, and in a sale through an agent there are three parties instead of two. The agent does not represent your interests but his own.

Furthermore, he said he could also make a more precise pre-selection regarding the creditworthiness of buyers through his connections to banks. I was surprised by the statement (keyword data protection?) but I wonder if there might actually be something to it.

“Connections” sounds shady to me. That he can learn from banks something they are not allowed to disclose sounds unbelievable to me. Maybe SCHUFA is possible for him, I don’t know. But you don’t need that either if you already put in the ad, maybe I’ll find my formulation for “if interested,” ...

Getting the sale done with as little hassle as possible would of course also be important to us. I consider myself sufficiently competent for photos, I could manage a sales text too. The time and coordination effort is probably still not to be underestimated.

You are probably mostly present when the interested parties come and you will presumably clean beforehand as well. For us, cleaning was the most unpleasant part, otherwise it was just small talk and sometimes drinking coffee with very, very nice people, some with sweet little children. :) Yes, it takes time, but it really can be very nice.

His first impression was quite positive, ... He makes a serious impression on me, that he doesn’t just blurt something out spontaneously.

That is his job, to make a positive first impression and appear serious.

And basically, he also cannot exclude the possibility that shortly before or at the notary appointment someone drops out due to a death or other reasons ... everyone has that right, including you.

You get security from the notary, not from the agent.

You don’t really want to know how long he practiced this dramaturgy in seminars and in front of the mirror ;-)

That would mean he attended seminars and thus probably already belongs to the top third of his profession. And yes, agents put in different amounts of effort. Some throw out a number after 5 minutes of review and others actually do some research.

I also wonder whether a price at a certain level has a higher chance of being achieved if the property is listed via an agent, than if I wrote the same price as a private person.

I see it rather the other way around. Buyers are glad to find an offer without an agent, since the high commission represents a psychological hurdle. Our buyers also repeatedly emphasized how glad they were that we sold without an agent, because the fees are crazy. Ultimately, the agent may directly cost you 20k, but in total it’s almost 40k. Buyers also have a budget limit and naturally mentally subtract the agent fees from it.

It all feels right, but I also feel sorry for the others. Since I have communicated openly with everyone from the beginning, I have informed them all of the current status. Everyone wants to wait and be contacted by me in case it doesn't work out with the first couple.

We did something similar. The feedback, even after the rejections, was without exception positive, because every other interested party found it very fair that we did not enter a bidding competition but, as promised from the beginning, the party that makes the first financially credible purchase commitment gets the house. It was a bit selfish, because I would have felt too guilty with a bidding competition, ;-) ... so by foregoing a bidding competition, I basically just bought my way out of my guilty conscience. But that's okay, a good conscience can sometimes cost something in euros. ;-)