House purchase - Experiences with open bidding process?

If the house is sold through a real estate agent, it usually goes to the highest bidder. Which is also in the agent’s interest because they then receive a higher commission.
If a house is sold privately, the decision might rather be based on who will get the house.
We bought our house privately. We were told to make an offer. But it wasn’t directly an auction process. The seller then decided who would get it.
We don’t know if we were the highest bidders. But we got the house even though we offered 15k less than the original asking price.
However, there were only a handful of interested parties because the house was not advertised on the internet or anything like that.

One should - which most people especially fail at when intending to use objects for themselves - stay grounded in values and think of their own interests (including those they might harm with their behavior!). Because what happens if, out of sheer irrationality, I stretch my creditworthiness to the breaking point and offer for a house - as beautiful as one may find it - as if the Amber Room were cast into the foundation, that is, if I offer ten thousand, twenty thousand, oh what am I saying, damn it, fifty thousand euros over the value?
Right - a competing bidder shows up who can outbid my irrationality even more extravagantly and throws the money around as if he were at the World Bank and got an employee discount. I haven't even finished saying "value plus fifty grand," and he loads his money-cases bazooka with "value plus eighty grand" and shoots me out of the race without a silencer.

What I have lost in the process is not only this oh so uniquely fantastic object. But I am still without supply and keep looking, quite possibly even in the neighboring town. And what do I have to listen to there? - again right: some idiot (ugh, was that me, who was said to look similar to me, damn, was that really me?) has driven prices in the region to astronomical heights. If I hadn’t opened my dumb mouth so wide and only offered ten grand over value, the nice competing bidder would have already outbid me with forty grand less, and I wouldn’t have driven my own price for the next object so insanely high. The other one would have gotten the contract cheaper, which I can’t care about, but I would have avoided scoring an own goal for myself.

So note two things:
1. no object is worth heating up the market for yourself;
2. "every end carries a beginning" also applies to bidding processes for houses. The sooner the next opportunity comes, the more excluded one lets oneself believe it is. Then every own goal avoided on the way counts, having not made it too expensive for yourself.

If relatives of certain risk groups - I like to call them the little demolition experts - show up somewhere, one should quickly switch from "bidding" to "staying cool, watching, and learning": the risk groups are brokers, communities of heirs, and bidders ready for any suicide mission.

Or to put it more briefly: when markets overheat, one should buy off the market.

During the private bidding process, the phone rang several times on Saturday noon asking if one wanted to increase the bid... That was annoying too. My husband might have bid further... I then got annoyed and stubborn and said stop

Something like that is absolutely unacceptable in my eyes. I even understand bidding processes with high interest, but harassing people afterwards goes too far.

some id*ot (oh, was that me, he is supposed to have looked like me, d... was that really me?) has driven prices in the region to astronomical heights.

But it always takes two to bid up. ;)
Otherwise, I have to point out: When I sell a house through an agent, I still decide who gets the contract. The agent may advise, but that's all he may do - at least with me.

250,000 euros estimated sale price + realtor commission + renovation work is actually already the limit for us.

Then offer exactly that. If you cannot do more, then that is just how it is. You should then expect not to get the contract.
And in many areas, 250k€ is practically nothing for a house. In my small city, a small 1930s semi-detached house was offered for 300k€. The advice was to tear the thing down and build new. So essentially it was only the land for that money, and the demolition costs come on top. Just as an example.

And, , don’t take it the wrong way... Your considerations still seem quite rudimentary. You have no idea yet what renovation costs will come your way. Are you sure a few cosmetic repairs will be enough? Or are there bigger issues with the old house?

If the bathroom still works, the renovation could also be postponed.