Pouring in screed insulation, yes or no?

I don't know how it looks for you, but usually the addressed widths can no longer be "simply" overlapped according to today's standards. It's not just about the gaps next to the pipes, but also about the width of the pipe route – together that's quickly 20 or 30 cm and that's definitely too much for cavities. I simply asked the screed layer at the time how he wanted it and then did it that way. Personally, I wouldn't start botching in such "sensitive" (and especially later no longer accessible) areas without a very good reason. But it's your house, you can do whatever you want :)

That is correct. In the mentioned room, however, there are a maximum of 2 25mm empty conduits side by side. So 5cm. Let's see, maybe I'll take that part again to make it perfect. However, I have the impression - regardless of the trade - that I apparently take everything more precisely than the construction workers. In this one room, I also wanted to be like "them" for once ;-)

However, I have the impression - regardless of the trade - that I apparently take everything more carefully than the construction workers.

You’re not alone ;-)

We almost installed the insulation under the screed ourselves throughout the entire house. Nice and neat with a polystyrene cutter and bonded backfill - tiptop!
In one room, however, the drywall installer wasn’t finished yet, so the heating engineers had to install the insulation there. They simply broke the boards and "somehow" laid them around the pipes and, despite gaps of up to 25cm in places, didn’t add any backfill. With much grumbling, they did it on my instruction and, after even more fuss, vacuumed the polystyrene afterwards.
Since they apparently didn’t take the vacuuming very seriously, we now have lots of inclusions of small polystyrene beads in the screed... and only there! :-(

So you're not alone ;-)

We installed the insulation under the screed ourselves in almost the entire house. Nicely done with a styrofoam cutter and bound loose fill - tiptop!
However, in one room the drywall installer was not finished yet, so the heating technicians had to lay the insulation there. They simply broke the panels and "somehow" laid them around the pipes and, despite gaps of up to 25cm in places, did not add any loose fill. With much grumbling, they completed it on my instruction and after even more fuss, they finally vacuumed up the styrofoam.
Since they probably didn’t take the vacuuming seriously, we now have lots of small styrofoam bead inclusions in the screed... and only there! :-(

We will also be installing the insulation ourselves in the next 2-3 weeks. Do I really need a styrofoam cutter, or is a utility knife sufficient?

A carpet knife/cutter is usually sufficient (depending on the thickness of the panels, however, the "sawing" can be quite annoying). However, you will spread a lot of styrofoam beads around the place, which should then be carefully vacuumed up for the reasons mentioned. I therefore recommend the styrofoam cutter.

A carpet knife/cutter is usually sufficient (depending on the thickness of the panels, the "sawing" can be quite annoying). However, you will scatter a lot of polystyrene beads around the place, which for the reasons mentioned should then be carefully vacuumed up again.
Therefore, I recommend the polystyrene cutter.

Or a jigsaw with a blade for styrofoam. I also find that very clean. It doesn’t smell as much either.

A cutter just makes way too much mess.