How much should a mid-terrace house cost per square meter today?

approximate loan amount of about 250-300K EUR.

This is the first idea.

I end up at 400K EUR

This is the second. And I still see that optimistically... A single-family house is worth more than a terraced middle house. And for the 300 m2 additional area/garden, I would rather not assume the standard ground value but less. It now depends on what you want. The landlord surely wants > 400,000 €. Is it worth it to you? Is it financeable? Does the landlord perhaps feel pressure and wants to take the quick/uncomplicated way before trying to sell a rented property. I would sleep on it again and try to coax the first figure out of the landlord’s nose to see if it even makes sense to continue calculating.

somewhere in the village in the deepest Saarland.

I offer 2 Lyoner sausages and a large bottle of Maggi. BTT: Did the landlord not drop any hints at all about what she expects? I never engage with such "what would you pay" dealers at the flea market. Your goods, you name a price. I see it similarly when buying a house. Whether you eventually agree can still be seen then?

What did the owner pay for it and how much of that have you (or other tenants) already paid off? That's what I would ask, and at the latest then the owner will laugh out loud and come up with a different price.

I see the question more like this: Do you really want to buy a house that you currently only like so-so? Especially with children, I find buying difficult because at first you need a bit more space, then suddenly a lot, and then no more. Sure, afterwards you can sell or rent it out, but in general it doesn’t sound like "Our dream house, we never want to leave here and we don’t want to be sued out because of personal use."

Regarding the rent: Currently about €1500 cold. If I convert that into an installment, I come to an approximate loan amount of about €250-300k at 4% interest and 3% repayment with a 20-year fixed interest rate.

You have to convert the cold rent to the interest only, not including repayment. Then you arrive at €450k financing.

With a 100 sqm plot and €500/sqm standard land value, I expect a significant upward adjustment of the land value. The land utilization will be extremely high. Maybe the plot is valued at €80,000-120,000 (? – no idea what correction factors are applied there).
The new build of 150 sqm living space currently costs between €450k and €525k. Then maybe another €30k-50k for ancillary construction costs and some for garden/terrace. So a new build should be somewhere around €550k-650k. Then you deduct depreciation for age – 7 years with 2% straight-line depreciation.

Then I roughly arrive at €475k-550k for the house including land. The location and thus the demand should be good at this standard land value. As a seller, I would probably start with a sales price somewhere between €550k and €600k.

With an actual purchase price of €550k + additional costs = €600k, that probably fits well. The cold rent corresponds to the interest rate – fits. Equity would then be €150k – a manageable 25%. In this respect, an attractive product on the market.

I am offering 2 Ring Lyoners and a large bottle of Maggi.

Maggi is apparently in short supply right now, it’s a valuable currency ;)

And I still see that optimistically...
A detached house is worth more than a terraced middle house.

And for the additional 300 m2 of area/garden, I would rather not assume the standard land value but less.

Now it depends on what you want. The landlord probably wants > 400,000 €. Is it worth it to you? Is it affordable?

Maybe the landlord is under pressure and wants to take the quick/uncomplicated route before trying to sell a rented property.

I would sleep on it again and try to get the first number out of the landlord’s mouth to see if it even makes sense to continue calculating.

I don’t understand: What do you mean by optimistic? If the detached house is worth more than the terraced middle house, that means my estimate is too high.
On the other hand: If the standard land value is set too high, that would mean my estimate is too low.

Whether 400,000 is affordable I have to clarify with the bank once there is a price on the table. Whether it’s worth it to us... Well, good question: If the subsequent landlord simply takes over the rental contract and we can easily live there for another 6 to 10 years until the kids get past the worst phase: no!
If the subsequent landlord files for personal use and wants us out and then we have to fight forever in court over hardship cases and notice periods so that our kids don’t get kicked out of daycare and in the end we would have to give up one of our two jobs: YES!

It’s quite possible that the landlady here is looking for the easy, quick way.

I offer 2 Ring Lyoner sausages and one large bottle of Maggi.

BTT: Has the landlady not hinted at all what she is expecting?
I never deal with those "what would you pay" dealers at flea markets. Your goods, you name the price.
I feel the same way about buying a house. Whether you end up agreeing can be seen later, right?

Unfortunately not yet: I also deliberately did not ask, because I first wanted to think independently of an already named number. I wanted to ask myself: What can I and what do I want to pay? Not: How can I conjure up amount X?

What she said was between the lines: It doesn't matter if I’m sending money to her or to the bank every month, which I translate as rent = purchase instalment.