Inherited equity, what to do, experiences?

I am in the minority here and mostly "pro terraced house";
The gardens only become nice after some years. Honestly, I hardly ever really look out of the window from the upper floor. I raise and lower the shutters, open and close the curtains, open and close the windows. But I don’t really sit there and look outside.

The children and you yourself are probably well connected in a new development area. Friendly communities form quickly.

The size of the garden is often overestimated when it comes to the children playing outside later. Children manage differently if the garden is small. The size of the garden is underestimated when it comes to the work involved. Gardening takes time. Even if you "only" have lawn (not recommended, needs lots of water and turns brown in summer). If you let the grass grow tall, even a small garden looks impressively green and nice but takes less work.
You yourselves say that you are busy with work and hardly have any time. What do you do then with the garden?

The homeowners’ association for the garages in the terraced house is really trivial: they vote on whether the LED lights should be with this or that lumen, where the wall boxes should be placed and which provider, which property manager handles everything. Those who want get involved a lot. Those who want get frustrated by the fact that they were outvoted on the LED lights; the communal part concerning parking is really nothing to fear in terms of community. Just pay and that’s it. :D

And one reason that is not unimportant to me: ecology and the landscape do not allow everyone to build a house with a big garden and area around it just because they don’t want to see "the people". I find that unacceptable in two respects to pass on to my children. I find living with a loose neighborhood community much better. But that is a matter of opinion.

I wouldn’t be put off by what is called a deterrent example of a terraced house here. And then you could even have the end house. That is a bit nicer than a middle house. Go for it, I’d say. Another advantage would be that you would hardly have to take on debt. Also, a terraced house can always be sold without problems. Demand is big and remains big, even in tight economic times.
It is different with detached houses (here in our region there are plenty of "ferments" to buy, detached, large, lots of land, mostly in need of renovation. Nobody buys those).

I would also make a lot dependent on the location. Commuting, driving the kids around, taking the car for every little thing really costs time (and money) and in my opinion also quality of life.

We bought a "young used" property. Our conditions were somewhat similar: no craftsmanship experience, little time for own work, and a foreseeable parental leave approaching. During this time, we had to tighten our belts considerably, especially towards the end, when we didn't have a childcare place (despite legal entitlement) and I therefore stayed at home a bit longer. We were therefore glad that we had not financed to the limit.

We didn't want a renovation project – not reliably calculable for us in terms of time and money. New construction was also out due to the costs, especially since there are hardly any plots available, and if there are, only at absolutely insane prices. The young used property was practically move-in ready, and we are gradually redesigning it; so far, these are only cosmetic/practical changes and therefore financially manageable. Of course, this means compromises in the "B-note": the equipment was not quite what we liked, and not everything on the outside was like our dream house. But you have to make compromises somewhere if you don't want to overstretch yourself, and except for the location, almost everything can be changed.

Maybe you should focus on something similar in your search? We gradually adjusted our criteria: from detached and condition from-to, to: maximum 10 years old, enough garden space, but a semi-detached house instead of a single-family house was also possible. After some searching, it then worked out in our desired location, of course. If you are not under time pressure, I wouldn't buy a compromise house, but only one in which you stand and feel "this is our new home." Our house was the only one during the search that immediately felt like us, apart from the matching key data. Therefore, I wouldn't just go by the pure numbers and facts, but also by feeling. After all, it is your own home.

I'll say it upfront: seeing around €350,000 in equity, but I don't see anything rosy at the moment when I read about €5,400, the horrendous prices in your area, and the desire to have children.

Well. I see two highly qualified young people with one child. Income from only one person. The second is not considered. Child benefits are also not considered. Plus moderate prices for a metropolitan city.
If, in addition to the €350,000 equity, another €350,000 is financed, it costs less than €2,000 per month. With these parameters, I maintain that the family is living on easy street.

qualified young people with a child.

… who are still planning to have offspring, where she will very likely not earn a significant additional income at first.

If, besides the €350,000 equity, another €350,000 is financed,

Yes, that then applies to the new build, but not to the existing properties, where a lot of euros still have to be invested.
They are not as handy as you are.
By the way, I also belong to Pro RH, DH or REH. I like all that, as has already listed. And WEG would not deter me either.

Being pampered is something else for me. Being pampered means: You have the choice!

Being laid on roses means something different to me. Being laid on roses means: You have the choice!

Yep. With total investment costs between €600,000 and €800,000, there are plenty of good existing buildings and new constructions. Even with one more child, the husband – she still doesn’t work – only has to spend a maximum of about one-third of his salary or the household income on the loan. And the family income can only continue to rise.
If this family doesn’t have the free choice, then who does?