Plot fully developed, additional costs?

Everything is correct...The section that is now with you from the coupling in the public area costs exactly 500 euros... As Andreas writes, be glad...usually it is much more because the lines usually do not lie on the properties but in front of them...fully developed is a flexible term.

Andreas, if you read properly, you would see that I wrote that the connections are already on my property

And what they say and what corresponds to the truth is also another matter. Many companies try to charge dumb customers twice. I see that regularly on my medical bills alone.

But since the issue apparently is not legally fixed, they can probably do whatever they want and I have to pay the nearly 700€

They did everything right...someone has to pay for the section from the coupling on the main cable in the street...this is actually always the builder, so you...even if the municipal utilities or whoever "laid it out"...you could now pin down your property seller on that, since you bought a developed property...maybe you're lucky and they will cover it...

Hahaha the seller is the city.
Do I have to write more?

You can try, but the chances of success are minimal...