Relocating the construction water connection yourself, what does the connection look like?

You can also use this for the base slab. For example, to wash out snow residues from the reinforcement or to clean the concrete pump.

You need the water more often than you think. I drilled a well right away with the money (a good 6" deep well for a proper pump was a bit more expensive), but I saved myself the column. Usually, neighbors already have a water connection. Before screed, plaster, and so on, the connections were logically inside the house; before that, I got something from the neighbor.

What exactly does the civil engineer need the water for?

There is a construction site toilet after all ;)

No, seriously. We have also experienced that on-site in practice much less or different is required than was initially demanded by the main contractor, etc.

We managed completely without our own construction water and construction electricity and were able to arrange everything with neighbors. Water was used very sparingly throughout the entire construction, and construction electricity hardly at all in the end.
Now, this does not answer Pinkiponk's question, but at that point I wouldn't worry either. Construction water and electricity are available, everything else should be solved by those on site...

There is of course a construction site toilet ;)

It works chemically and is regularly serviced by the service vehicle.

We did not provide any construction water at all. Concrete is delivered ready-made anyway, the shell builder had an IBC container on the flatbed to mix the adhesive, which doesn't require much.
Trades like screed or geothermal drilling bring their own standpipe anyway if there is no water in the house yet, since it is only needed for a few days and they need water every day on their changing construction sites. It doesn't make sense to have someone else provide it.

Works through chemistry and is regularly serviced by the service vehicle.

Oh, you also think that a sandwich tastes better with unwashed hands!? :p

Oh, you also think that the sandwich tastes better with unwashed hands!? :p

As I said, no one sets up a standpipe for just a few liters a day. How do you think that would work if in the new development "everyone" constantly wants to connect a standpipe? No way. Apart from the insane costs. There's an IBC container for that and that's it, or bottled water.