Does the heat pump need to be installed, 5.5m for €999 justified?

Sounds suspiciously like "We don't care where it is located, but we'll just add a thousand euros. We don't have extra work or material costs, but we'll take the money anyway..." 999,- euros. Who came up with this Möbel-Hübner price?

At 999,-€? I can tell you exactly how that amount is made up. ;-)
"Hey boss, how much?"
"Keep it under a thousand, or he'll complain!"
"Ok."

And that is exactly why he should ask, because it sounds very much like a flat rate.

Otherwise, this is simply a usual general contractor pricing for changes after contract conclusion. It’s not just about the additional meters of refrigeration piping but about the effort involved in deviating from the standard.

Does anyone know how sound insulation works? Is it a basis for the building application or just something nice for the neighbor?

That is regulated by law. The sound level at the boundary may only be a certain loudness.

First of all, thank you for your extensive answers! We also believe that this is simply the usual price gouging for additional work.

In the meantime, we have even coordinated briefly with our new neighbors; for them, the location of the pump would be absolutely irrelevant since their bedroom faces the other side.

Now our question would be whether the location of the pump is not legally allowed there "because of this sound radius" or whether these are more recommendations and can be dismissed.

In the latter case, we would leave the pump where it costs us nothing and just deal with it.

The sound emissions are legally regulated and part of the building permit; they are often not checked, but eventually someone will be bothered by it. Whether the price is justified depends on many factors. Installation inside the house at the same location, then it is only a few meters of cable, which must be covered. New opening in a planned prefabricated basement, then the price is appropriate.