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

Yes and no. I believe that many sellers would definitely do without brokers if they received the invoice for the full amount. And the rest would place more value on it. You can also see the effect when the "bestellerprinzip" was introduced for rental apartments. Of course, in the end, it all gets passed on again, but it would also clarify the front lines. The broker is then clearly only responsible for the seller and maximizes their revenue.

I can only share my experience: we sold 3 houses:
1.) without a broker (we already had a private buyer lined up). Went smoothly. But we felt that we could have achieved a higher selling price.
2.) with broker A. That was a deal. The broker received commissions from both parties. It was okay. The sale went through fairly quickly, the price was market-appropriate.
3.) with broker B. He advised us to bear the entire broker commission as sellers. We did that, but—let’s say—in a somewhat different payment model than usual (minimal commission on sale at market value, substantial participation on every euro above that). In the end, we sold the house significantly above value, the broker sent a hefty invoice (ultimately 8% of the selling price), and the buyers were happy because they paid no broker fee.

Prices are, of course, always a subjective matter and cannot be objectively verified. I would work with broker B again.

Prices are, of course, always a subjective matter and cannot be objectively verified.

Exactly. Expert reports can never be more than an aid to argument; the decision to agree to the proposed price or not can only be made by the two negotiating partners. And even there, the bank usually has the final say, since few market participants put amounts of such magnitude on the table from their own liquidity. This has recently probably been the most common reason for failure: the seller calls for the appraised value plus a generous goodwill premium, the buyer is willing to swallow the bitter pill, but his financing bank then says, "You must be crazy."

but his financing bank then says "You must be crazy".

Partly with good reason, presumably?
The bank is not the evil enemy as it is often portrayed. The bank wants to take as little risk as possible that it will be left with a loss if something goes wrong with the contractual relationship. That means the loan amount must be backed by a certain value.

The bank might lowball it a bit to avoid taking a risk. But the customer will also bring in some equity – and the bank usually doesn’t care whether you blow it or not. So if the bank, despite the equity contribution, says "the house is not worth the loan," then as a consumer I would also consider whether it is worth putting my hard-earned money into it?

I'll write somewhere: Buying, selling, and building a house are highly emotional, usually involve a lot of money, and you want to live in it for years. The bank naturally sees it differently. It doesn't benefit from having to auction off y houses in x years.