How do you assess this house? How much budget will be necessary?

I wouldn’t even do an ETICS in front of the facade if it was given to me for free.

I am definitely not an advocate of facade insulation and even less so of ETICS – but built in 1940 and the exterior view screams for 24cm double brick row, U-value of 1.5 - 2.0 W/m²K. You can do that, not only because of pure energy savings but also for comfort reasons and to prevent condensation/mold... with a different wall structure you have to weigh it up.

I don’t understand why you always make heating systems so expensive?
My neighbor paid 2.5k for his completely new heating system (Vaillant gas). I looked online once. These things are not that expensive.

Clay roof tiles are also available online for under €10/m². No one has ever roofed a roof for me at that price.
Gas boiler system completely including connection from the meter and renewing the flue under €5,000 without own work – I would like to see that with an invoice, please. Usually, a lot of extras come on top of the online prices (wall brackets, connection pieces, shut-off devices, safety group, expansion vessel, hot water storage tank, control module with outdoor temperature sensor, possibly hot water circulation pump, DVGW drinking water filter with backflow preventer, Spiro trap, PE/aluminum chimney), and the plumber also expects payment (minimum 10 hours including dismantling). And I have never seen an invoice under €5,000 for that, and I see quite a few. Most lie between €6,000 and €8,000 for gas. Oil is usually about €1,000 more.
For my own old house, the plumber got €20,000 from me (12 radiators, 20m² underfloor heating in bath and kitchen including screed, GB boiler 20kW + hot water storage, circulation, approx. 20m piping hot+cold surface mounted and all radiator pipes, partial own work as boxing in as well as wastewater pipes in the house with two air vents and all supply lines to bathroom ceramics, 2 pre-wall elements for WC as well as bathtub and shower tray installation) and I had offers between 20k and 30k. Just as a reference for the questioner.

Our Viessmann in the old RH cost about 8000 around 10 years ago. You need this and that... so that everything new fits with the old. Of course including installation.

The seller still hasn't gotten in touch. A phone number is not provided in the listing.

Nevertheless, I have received many important tips that I can keep using again and again!

Thanks again!

Write when the time comes.
We are eager to see how the story continues in Bremen.

If they treated the other interested parties the same way, I am no longer surprised why the cabin was not sold and the price keeps dropping.

Write when the time comes. We are curious to see how the story in Bremen continues

There is currently nothing new. The seller has not reported back and probably will not do so anymore.